package scipy

  1. Overview
  2. Docs
package scipy
Legend:
Library
Module
Module type
Parameter
Class
Class type
val get_py : string -> Py.Object.t

Get an attribute of this module as a Py.Object.t. This is useful to pass a Python function to another function.

module Filters : sig ... end
module Fourier : sig ... end
module Interpolation : sig ... end
module Measurements : sig ... end
module Morphology : sig ... end
val affine_transform : ?offset:[ `F of float | `Sequence of Py.Object.t ] -> ?output_shape:int list -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?order:int -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?prefilter:bool -> input:[> `Ndarray ] Np.Obj.t -> matrix:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Apply an affine transformation.

Given an output image pixel index vector ``o``, the pixel value is determined from the input image at position ``np.dot(matrix, o) + offset``.

This does 'pull' (or 'backward') resampling, transforming the output space to the input to locate data. Affine transformations are often described in the 'push' (or 'forward') direction, transforming input to output. If you have a matrix for the 'push' transformation, use its inverse (:func:`numpy.linalg.inv`) in this function.

Parameters ---------- input : array_like The input array. matrix : ndarray The inverse coordinate transformation matrix, mapping output coordinates to input coordinates. If ``ndim`` is the number of dimensions of ``input``, the given matrix must have one of the following shapes:

  • ``(ndim, ndim)``: the linear transformation matrix for each output coordinate.
  • ``(ndim,)``: assume that the 2-D transformation matrix is diagonal, with the diagonal specified by the given value. A more efficient algorithm is then used that exploits the separability of the problem.
  • ``(ndim + 1, ndim + 1)``: assume that the transformation is specified using homogeneous coordinates 1_. In this case, any value passed to ``offset`` is ignored.
  • ``(ndim, ndim + 1)``: as above, but the bottom row of a homogeneous transformation matrix is always ``0, 0, ..., 1``, and may be omitted.

offset : float or sequence, optional The offset into the array where the transform is applied. If a float, `offset` is the same for each axis. If a sequence, `offset` should contain one value for each axis. output_shape : tuple of ints, optional Shape tuple. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with `spline_filter` before interpolation. The default is True, which will create a temporary `float64` array of filtered values if `order > 1`. If setting this to False, the output will be slightly blurred if `order > 1`, unless the input is prefiltered, i.e. it is the result of calling `spline_filter` on the original input.

Returns ------- affine_transform : ndarray The transformed input.

Notes ----- The given matrix and offset are used to find for each point in the output the corresponding coordinates in the input by an affine transformation. The value of the input at those coordinates is determined by spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode.

.. versionchanged:: 0.18.0 Previously, the exact interpretation of the affine transformation depended on whether the matrix was supplied as a 1-D or a 2-D array. If a 1-D array was supplied to the matrix parameter, the output pixel value at index ``o`` was determined from the input image at position ``matrix * (o + offset)``.

References ---------- .. 1 https://en.wikipedia.org/wiki/Homogeneous_coordinates

val binary_closing : ?structure:[> `Ndarray ] Np.Obj.t -> ?iterations:int -> ?output:[> `Ndarray ] Np.Obj.t -> ?origin:int list -> ?mask:[> `Ndarray ] Np.Obj.t -> ?border_value:int -> ?brute_force:bool -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Multidimensional binary closing with the given structuring element.

The *closing* of an input image by a structuring element is the *erosion* of the *dilation* of the image by the structuring element.

Parameters ---------- input : array_like Binary array_like to be closed. Non-zero (True) elements form the subset to be closed. structure : array_like, optional Structuring element used for the closing. Non-zero elements are considered True. If no structuring element is provided an element is generated with a square connectivity equal to one (i.e., only nearest neighbors are connected to the center, diagonally-connected elements are not considered neighbors). iterations : int, optional The dilation step of the closing, then the erosion step are each repeated `iterations` times (one, by default). If iterations is less than 1, each operations is repeated until the result does not change anymore. Only an integer of iterations is accepted. output : ndarray, optional Array of the same shape as input, into which the output is placed. By default, a new array is created. origin : int or tuple of ints, optional Placement of the filter, by default 0. mask : array_like, optional If a mask is given, only those elements with a True value at the corresponding mask element are modified at each iteration.

.. versionadded:: 1.1.0 border_value : int (cast to 0 or 1), optional Value at the border in the output array.

.. versionadded:: 1.1.0 brute_force : boolean, optional Memory condition: if False, only the pixels whose value was changed in the last iteration are tracked as candidates to be updated in the current iteration; if true al pixels are considered as candidates for update, regardless of what happened in the previous iteration. False by default.

.. versionadded:: 1.1.0

Returns ------- binary_closing : ndarray of bools Closing of the input by the structuring element.

See also -------- grey_closing, binary_opening, binary_dilation, binary_erosion, generate_binary_structure

Notes ----- *Closing* 1_ is a mathematical morphology operation 2_ that consists in the succession of a dilation and an erosion of the input with the same structuring element. Closing therefore fills holes smaller than the structuring element.

Together with *opening* (`binary_opening`), closing can be used for noise removal.

References ---------- .. 1 https://en.wikipedia.org/wiki/Closing_%28morphology%29 .. 2 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((5,5), dtype=int) >>> a1:-1, 1:-1 = 1; a2,2 = 0 >>> a array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]) >>> # Closing removes small holes >>> ndimage.binary_closing(a).astype(int) array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]) >>> # Closing is the erosion of the dilation of the input >>> ndimage.binary_dilation(a).astype(int) array([0, 1, 1, 1, 0], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [0, 1, 1, 1, 0]) >>> ndimage.binary_erosion(ndimage.binary_dilation(a)).astype(int) array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0])

>>> a = np.zeros((7,7), dtype=int) >>> a1:6, 2:5 = 1; a1:3,3 = 0 >>> a array([0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> # In addition to removing holes, closing can also >>> # coarsen boundaries with fine hollows. >>> ndimage.binary_closing(a).astype(int) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> ndimage.binary_closing(a, structure=np.ones((2,2))).astype(int) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0])

val binary_dilation : ?structure:[> `Ndarray ] Np.Obj.t -> ?iterations:int -> ?mask:[> `Ndarray ] Np.Obj.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?border_value:int -> ?origin:int list -> ?brute_force:bool -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Multidimensional binary dilation with the given structuring element.

Parameters ---------- input : array_like Binary array_like to be dilated. Non-zero (True) elements form the subset to be dilated. structure : array_like, optional Structuring element used for the dilation. Non-zero elements are considered True. If no structuring element is provided an element is generated with a square connectivity equal to one. iterations : int, optional The dilation is repeated `iterations` times (one, by default). If iterations is less than 1, the dilation is repeated until the result does not change anymore. Only an integer of iterations is accepted. mask : array_like, optional If a mask is given, only those elements with a True value at the corresponding mask element are modified at each iteration. output : ndarray, optional Array of the same shape as input, into which the output is placed. By default, a new array is created. border_value : int (cast to 0 or 1), optional Value at the border in the output array. origin : int or tuple of ints, optional Placement of the filter, by default 0. brute_force : boolean, optional Memory condition: if False, only the pixels whose value was changed in the last iteration are tracked as candidates to be updated (dilated) in the current iteration; if True all pixels are considered as candidates for dilation, regardless of what happened in the previous iteration. False by default.

Returns ------- binary_dilation : ndarray of bools Dilation of the input by the structuring element.

See also -------- grey_dilation, binary_erosion, binary_closing, binary_opening, generate_binary_structure

Notes ----- Dilation 1_ is a mathematical morphology operation 2_ that uses a structuring element for expanding the shapes in an image. The binary dilation of an image by a structuring element is the locus of the points covered by the structuring element, when its center lies within the non-zero points of the image.

References ---------- .. 1 https://en.wikipedia.org/wiki/Dilation_%28morphology%29 .. 2 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((5, 5)) >>> a2, 2 = 1 >>> a array([ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 1., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.]) >>> ndimage.binary_dilation(a) array([False, False, False, False, False], [False, False, True, False, False], [False, True, True, True, False], [False, False, True, False, False], [False, False, False, False, False], dtype=bool) >>> ndimage.binary_dilation(a).astype(a.dtype) array([ 0., 0., 0., 0., 0.], [ 0., 0., 1., 0., 0.], [ 0., 1., 1., 1., 0.], [ 0., 0., 1., 0., 0.], [ 0., 0., 0., 0., 0.]) >>> # 3x3 structuring element with connectivity 1, used by default >>> struct1 = ndimage.generate_binary_structure(2, 1) >>> struct1 array([False, True, False], [ True, True, True], [False, True, False], dtype=bool) >>> # 3x3 structuring element with connectivity 2 >>> struct2 = ndimage.generate_binary_structure(2, 2) >>> struct2 array([ True, True, True], [ True, True, True], [ True, True, True], dtype=bool) >>> ndimage.binary_dilation(a, structure=struct1).astype(a.dtype) array([ 0., 0., 0., 0., 0.], [ 0., 0., 1., 0., 0.], [ 0., 1., 1., 1., 0.], [ 0., 0., 1., 0., 0.], [ 0., 0., 0., 0., 0.]) >>> ndimage.binary_dilation(a, structure=struct2).astype(a.dtype) array([ 0., 0., 0., 0., 0.], [ 0., 1., 1., 1., 0.], [ 0., 1., 1., 1., 0.], [ 0., 1., 1., 1., 0.], [ 0., 0., 0., 0., 0.]) >>> ndimage.binary_dilation(a, structure=struct1,\ ... iterations=2).astype(a.dtype) array([ 0., 0., 1., 0., 0.], [ 0., 1., 1., 1., 0.], [ 1., 1., 1., 1., 1.], [ 0., 1., 1., 1., 0.], [ 0., 0., 1., 0., 0.])

val binary_erosion : ?structure:[> `Ndarray ] Np.Obj.t -> ?iterations:int -> ?mask:[> `Ndarray ] Np.Obj.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?border_value:int -> ?origin:int list -> ?brute_force:bool -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Multidimensional binary erosion with a given structuring element.

Binary erosion is a mathematical morphology operation used for image processing.

Parameters ---------- input : array_like Binary image to be eroded. Non-zero (True) elements form the subset to be eroded. structure : array_like, optional Structuring element used for the erosion. Non-zero elements are considered True. If no structuring element is provided, an element is generated with a square connectivity equal to one. iterations : int, optional The erosion is repeated `iterations` times (one, by default). If iterations is less than 1, the erosion is repeated until the result does not change anymore. mask : array_like, optional If a mask is given, only those elements with a True value at the corresponding mask element are modified at each iteration. output : ndarray, optional Array of the same shape as input, into which the output is placed. By default, a new array is created. border_value : int (cast to 0 or 1), optional Value at the border in the output array. origin : int or tuple of ints, optional Placement of the filter, by default 0. brute_force : boolean, optional Memory condition: if False, only the pixels whose value was changed in the last iteration are tracked as candidates to be updated (eroded) in the current iteration; if True all pixels are considered as candidates for erosion, regardless of what happened in the previous iteration. False by default.

Returns ------- binary_erosion : ndarray of bools Erosion of the input by the structuring element.

See also -------- grey_erosion, binary_dilation, binary_closing, binary_opening, generate_binary_structure

Notes ----- Erosion 1_ is a mathematical morphology operation 2_ that uses a structuring element for shrinking the shapes in an image. The binary erosion of an image by a structuring element is the locus of the points where a superimposition of the structuring element centered on the point is entirely contained in the set of non-zero elements of the image.

References ---------- .. 1 https://en.wikipedia.org/wiki/Erosion_%28morphology%29 .. 2 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((7,7), dtype=int) >>> a1:6, 2:5 = 1 >>> a array([0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> ndimage.binary_erosion(a).astype(a.dtype) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> #Erosion removes objects smaller than the structure >>> ndimage.binary_erosion(a, structure=np.ones((5,5))).astype(a.dtype) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0])

val binary_fill_holes : ?structure:[> `Ndarray ] Np.Obj.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?origin:int list -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Fill the holes in binary objects.

Parameters ---------- input : array_like N-D binary array with holes to be filled structure : array_like, optional Structuring element used in the computation; large-size elements make computations faster but may miss holes separated from the background by thin regions. The default element (with a square connectivity equal to one) yields the intuitive result where all holes in the input have been filled. output : ndarray, optional Array of the same shape as input, into which the output is placed. By default, a new array is created. origin : int, tuple of ints, optional Position of the structuring element.

Returns ------- out : ndarray Transformation of the initial image `input` where holes have been filled.

See also -------- binary_dilation, binary_propagation, label

Notes ----- The algorithm used in this function consists in invading the complementary of the shapes in `input` from the outer boundary of the image, using binary dilations. Holes are not connected to the boundary and are therefore not invaded. The result is the complementary subset of the invaded region.

References ---------- .. 1 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((5, 5), dtype=int) >>> a1:4, 1:4 = 1 >>> a2,2 = 0 >>> a array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]) >>> ndimage.binary_fill_holes(a).astype(int) array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]) >>> # Too big structuring element >>> ndimage.binary_fill_holes(a, structure=np.ones((5,5))).astype(int) array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0])

val binary_hit_or_miss : ?structure1:[> `Ndarray ] Np.Obj.t -> ?structure2:[> `Ndarray ] Np.Obj.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?origin1:int list -> ?origin2:int list -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional binary hit-or-miss transform.

The hit-or-miss transform finds the locations of a given pattern inside the input image.

Parameters ---------- input : array_like (cast to booleans) Binary image where a pattern is to be detected. structure1 : array_like (cast to booleans), optional Part of the structuring element to be fitted to the foreground (non-zero elements) of `input`. If no value is provided, a structure of square connectivity 1 is chosen. structure2 : array_like (cast to booleans), optional Second part of the structuring element that has to miss completely the foreground. If no value is provided, the complementary of `structure1` is taken. output : ndarray, optional Array of the same shape as input, into which the output is placed. By default, a new array is created. origin1 : int or tuple of ints, optional Placement of the first part of the structuring element `structure1`, by default 0 for a centered structure. origin2 : int or tuple of ints, optional Placement of the second part of the structuring element `structure2`, by default 0 for a centered structure. If a value is provided for `origin1` and not for `origin2`, then `origin2` is set to `origin1`.

Returns ------- binary_hit_or_miss : ndarray Hit-or-miss transform of `input` with the given structuring element (`structure1`, `structure2`).

See also -------- binary_erosion

References ---------- .. 1 https://en.wikipedia.org/wiki/Hit-or-miss_transform

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((7,7), dtype=int) >>> a1, 1 = 1; a2:4, 2:4 = 1; a4:6, 4:6 = 1 >>> a array([0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]) >>> structure1 = np.array([1, 0, 0], [0, 1, 1], [0, 1, 1]) >>> structure1 array([1, 0, 0], [0, 1, 1], [0, 1, 1]) >>> # Find the matches of structure1 in the array a >>> ndimage.binary_hit_or_miss(a, structure1=structure1).astype(int) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> # Change the origin of the filter >>> # origin1=1 is equivalent to origin1=(1,1) here >>> ndimage.binary_hit_or_miss(a, structure1=structure1,\ ... origin1=1).astype(int) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0])

val binary_opening : ?structure:[> `Ndarray ] Np.Obj.t -> ?iterations:int -> ?output:[> `Ndarray ] Np.Obj.t -> ?origin:int list -> ?mask:[> `Ndarray ] Np.Obj.t -> ?border_value:int -> ?brute_force:bool -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Multidimensional binary opening with the given structuring element.

The *opening* of an input image by a structuring element is the *dilation* of the *erosion* of the image by the structuring element.

Parameters ---------- input : array_like Binary array_like to be opened. Non-zero (True) elements form the subset to be opened. structure : array_like, optional Structuring element used for the opening. Non-zero elements are considered True. If no structuring element is provided an element is generated with a square connectivity equal to one (i.e., only nearest neighbors are connected to the center, diagonally-connected elements are not considered neighbors). iterations : int, optional The erosion step of the opening, then the dilation step are each repeated `iterations` times (one, by default). If `iterations` is less than 1, each operation is repeated until the result does not change anymore. Only an integer of iterations is accepted. output : ndarray, optional Array of the same shape as input, into which the output is placed. By default, a new array is created. origin : int or tuple of ints, optional Placement of the filter, by default 0. mask : array_like, optional If a mask is given, only those elements with a True value at the corresponding mask element are modified at each iteration.

.. versionadded:: 1.1.0 border_value : int (cast to 0 or 1), optional Value at the border in the output array.

.. versionadded:: 1.1.0 brute_force : boolean, optional Memory condition: if False, only the pixels whose value was changed in the last iteration are tracked as candidates to be updated in the current iteration; if true all pixels are considered as candidates for update, regardless of what happened in the previous iteration. False by default.

.. versionadded:: 1.1.0

Returns ------- binary_opening : ndarray of bools Opening of the input by the structuring element.

See also -------- grey_opening, binary_closing, binary_erosion, binary_dilation, generate_binary_structure

Notes ----- *Opening* 1_ is a mathematical morphology operation 2_ that consists in the succession of an erosion and a dilation of the input with the same structuring element. Opening, therefore, removes objects smaller than the structuring element.

Together with *closing* (`binary_closing`), opening can be used for noise removal.

References ---------- .. 1 https://en.wikipedia.org/wiki/Opening_%28morphology%29 .. 2 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((5,5), dtype=int) >>> a1:4, 1:4 = 1; a4, 4 = 1 >>> a array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 1]) >>> # Opening removes small objects >>> ndimage.binary_opening(a, structure=np.ones((3,3))).astype(int) array([0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]) >>> # Opening can also smooth corners >>> ndimage.binary_opening(a).astype(int) array([0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 1, 1, 1, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0]) >>> # Opening is the dilation of the erosion of the input >>> ndimage.binary_erosion(a).astype(int) array([0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]) >>> ndimage.binary_dilation(ndimage.binary_erosion(a)).astype(int) array([0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 1, 1, 1, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0])

val binary_propagation : ?structure:[> `Ndarray ] Np.Obj.t -> ?mask:[> `Ndarray ] Np.Obj.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?border_value:int -> ?origin:int list -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional binary propagation with the given structuring element.

Parameters ---------- input : array_like Binary image to be propagated inside `mask`. structure : array_like, optional Structuring element used in the successive dilations. The output may depend on the structuring element, especially if `mask` has several connex components. If no structuring element is provided, an element is generated with a squared connectivity equal to one. mask : array_like, optional Binary mask defining the region into which `input` is allowed to propagate. output : ndarray, optional Array of the same shape as input, into which the output is placed. By default, a new array is created. border_value : int (cast to 0 or 1), optional Value at the border in the output array. origin : int or tuple of ints, optional Placement of the filter, by default 0.

Returns ------- binary_propagation : ndarray Binary propagation of `input` inside `mask`.

Notes ----- This function is functionally equivalent to calling binary_dilation with the number of iterations less than one: iterative dilation until the result does not change anymore.

The succession of an erosion and propagation inside the original image can be used instead of an *opening* for deleting small objects while keeping the contours of larger objects untouched.

References ---------- .. 1 http://cmm.ensmp.fr/~serra/cours/pdf/en/ch6en.pdf, slide 15. .. 2 I.T. Young, J.J. Gerbrands, and L.J. van Vliet, 'Fundamentals of image processing', 1998 ftp://qiftp.tudelft.nl/DIPimage/docs/FIP2.3.pdf

Examples -------- >>> from scipy import ndimage >>> input = np.zeros((8, 8), dtype=int) >>> input2, 2 = 1 >>> mask = np.zeros((8, 8), dtype=int) >>> mask1:4, 1:4 = mask4, 4 = mask6:8, 6:8 = 1 >>> input array([0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]) >>> mask array([0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 1]) >>> ndimage.binary_propagation(input, mask=mask).astype(int) array([0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]) >>> ndimage.binary_propagation(input, mask=mask,\ ... structure=np.ones((3,3))).astype(int) array([0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0])

>>> # Comparison between opening and erosion+propagation >>> a = np.zeros((6,6), dtype=int) >>> a2:5, 2:5 = 1; a0, 0 = 1; a5, 5 = 1 >>> a array([1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 1]) >>> ndimage.binary_opening(a).astype(int) array([0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0]) >>> b = ndimage.binary_erosion(a) >>> b.astype(int) array([0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]) >>> ndimage.binary_propagation(b, mask=a).astype(int) array([0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0])

val black_tophat : ?size:int list -> ?footprint:Py.Object.t -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional black tophat filter.

Parameters ---------- input : array_like Input. size : tuple of ints, optional Shape of a flat and full structuring element used for the filter. Optional if `footprint` or `structure` is provided. footprint : array of ints, optional Positions of non-infinite elements of a flat structuring element used for the black tophat filter. structure : array of ints, optional Structuring element used for the filter. `structure` may be a non-flat structuring element. output : array, optional An array used for storing the output of the filter may be provided. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the array borders are handled, where `cval` is the value when mode is equal to 'constant'. Default is 'reflect' cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : scalar, optional The `origin` parameter controls the placement of the filter. Default 0

Returns ------- black_tophat : ndarray Result of the filter of `input` with `structure`.

See also -------- white_tophat, grey_opening, grey_closing

val center_of_mass : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[ `I of int | `Is of int list ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate the center of mass of the values of an array at labels.

Parameters ---------- input : ndarray Data from which to calculate center-of-mass. The masses can either be positive or negative. labels : ndarray, optional Labels for objects in `input`, as generated by `ndimage.label`. Only used with `index`. Dimensions must be the same as `input`. index : int or sequence of ints, optional Labels for which to calculate centers-of-mass. If not specified, all labels greater than zero are used. Only used with `labels`.

Returns ------- center_of_mass : tuple, or list of tuples Coordinates of centers-of-mass.

Examples -------- >>> a = np.array((0,0,0,0, ... 0,1,1,0, ... 0,1,1,0, ... 0,1,1,0)) >>> from scipy import ndimage >>> ndimage.measurements.center_of_mass(a) (2.0, 1.5)

Calculation of multiple objects in an image

>>> b = np.array((0,1,1,0, ... 0,1,0,0, ... 0,0,0,0, ... 0,0,1,1, ... 0,0,1,1)) >>> lbl = ndimage.label(b)0 >>> ndimage.measurements.center_of_mass(b, lbl, 1,2) (0.33333333333333331, 1.3333333333333333), (3.5, 2.5)

Negative masses are also accepted, which can occur for example when bias is removed from measured data due to random noise.

>>> c = np.array((-1,0,0,0, ... 0,-1,-1,0, ... 0,1,-1,0, ... 0,1,1,0)) >>> ndimage.measurements.center_of_mass(c) (-4.0, 1.0)

If there are division by zero issues, the function does not raise an error but rather issues a RuntimeWarning before returning inf and/or NaN.

>>> d = np.array(-1, 1) >>> ndimage.measurements.center_of_mass(d) (inf,)

val convolve : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> weights:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional convolution.

The array is convolved with the given kernel.

Parameters ---------- input : array_like The input array. weights : array_like Array of weights, same number of dimensions as input output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0 origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- result : ndarray The result of convolution of `input` with `weights`.

See Also -------- correlate : Correlate an image with a kernel.

Notes ----- Each value in result is :math:`C_i = \sum_jI_{i+k-j W_j

}

`, where W is the `weights` kernel, j is the N-D spatial index over :math:`W`, I is the `input` and k is the coordinate of the center of W, specified by `origin` in the input parameters.

Examples -------- Perhaps the simplest case to understand is ``mode='constant', cval=0.0``, because in this case borders (i.e., where the `weights` kernel, centered on any one value, extends beyond an edge of `input`) are treated as zeros.

>>> a = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> k = np.array([1,1,1],[1,1,0],[1,0,0]) >>> from scipy import ndimage >>> ndimage.convolve(a, k, mode='constant', cval=0.0) array([11, 10, 7, 4], [10, 3, 11, 11], [15, 12, 14, 7], [12, 3, 7, 0])

Setting ``cval=1.0`` is equivalent to padding the outer edge of `input` with 1.0's (and then extracting only the original region of the result).

>>> ndimage.convolve(a, k, mode='constant', cval=1.0) array([13, 11, 8, 7], [11, 3, 11, 14], [16, 12, 14, 10], [15, 6, 10, 5])

With ``mode='reflect'`` (the default), outer values are reflected at the edge of `input` to fill in missing values.

>>> b = np.array([2, 0, 0], ... [1, 0, 0], ... [0, 0, 0]) >>> k = np.array([0,1,0], [0,1,0], [0,1,0]) >>> ndimage.convolve(b, k, mode='reflect') array([5, 0, 0], [3, 0, 0], [1, 0, 0])

This includes diagonally at the corners.

>>> k = np.array([1,0,0],[0,1,0],[0,0,1]) >>> ndimage.convolve(b, k) array([4, 2, 0], [3, 2, 0], [1, 1, 0])

With ``mode='nearest'``, the single nearest value in to an edge in `input` is repeated as many times as needed to match the overlapping `weights`.

>>> c = np.array([2, 0, 1], ... [1, 0, 0], ... [0, 0, 0]) >>> k = np.array([0, 1, 0], ... [0, 1, 0], ... [0, 1, 0], ... [0, 1, 0], ... [0, 1, 0]) >>> ndimage.convolve(c, k, mode='nearest') array([7, 0, 3], [5, 0, 2], [3, 0, 1])

val convolve1d : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:int -> input:[> `Ndarray ] Np.Obj.t -> weights:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a 1-D convolution along the given axis.

The lines of the array along the given axis are convolved with the given weights.

Parameters ---------- input : array_like The input array. weights : ndarray 1-D sequence of numbers. axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right.

Returns ------- convolve1d : ndarray Convolved array with same shape as input

Examples -------- >>> from scipy.ndimage import convolve1d >>> convolve1d(2, 8, 0, 4, 1, 9, 9, 0, weights=1, 3) array(14, 24, 4, 13, 12, 36, 27, 0)

val correlate : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> weights:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional correlation.

The array is correlated with the given kernel.

Parameters ---------- input : array_like The input array. weights : ndarray array of weights, same number of dimensions as input output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- result : ndarray The result of correlation of `input` with `weights`.

See Also -------- convolve : Convolve an image with a kernel.

Examples -------- Correlation is the process of moving a filter mask often referred to as kernel over the image and computing the sum of products at each location.

>>> from scipy.ndimage import correlate >>> input_img = np.arange(25).reshape(5,5) >>> print(input_img) [ 0 1 2 3 4] [ 5 6 7 8 9] [10 11 12 13 14] [15 16 17 18 19] [20 21 22 23 24]

Define a kernel (weights) for correlation. In this example, it is for sum of center and up, down, left and right next elements.

>>> weights = [0, 1, 0], ... [1, 1, 1], ... [0, 1, 0]

We can calculate a correlation result: For example, element ``2,2`` is ``7 + 11 + 12 + 13 + 17 = 60``.

>>> correlate(input_img, weights) array([ 6, 10, 15, 20, 24], [ 26, 30, 35, 40, 44], [ 51, 55, 60, 65, 69], [ 76, 80, 85, 90, 94], [ 96, 100, 105, 110, 114])

val correlate1d : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:int -> input:[> `Ndarray ] Np.Obj.t -> weights:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate a 1-D correlation along the given axis.

The lines of the array along the given axis are correlated with the given weights.

Parameters ---------- input : array_like The input array. weights : array 1-D sequence of numbers. axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right.

Examples -------- >>> from scipy.ndimage import correlate1d >>> correlate1d(2, 8, 0, 4, 1, 9, 9, 0, weights=1, 3) array( 8, 26, 8, 12, 7, 28, 36, 9)

val distance_transform_bf : ?metric:string -> ?sampling:[ `I of int | `Is of int list ] -> ?return_distances:bool -> ?return_indices:bool -> ?distances:Py.Object.t -> ?indices:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t * [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Distance transform function by a brute force algorithm.

This function calculates the distance transform of the `input`, by replacing each foreground (non-zero) element, with its shortest distance to the background (any zero-valued element).

In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element is returned along the first axis of the result.

Parameters ---------- input : array_like Input metric : str, optional Three types of distance metric are supported: 'euclidean', 'taxicab', and 'chessboard'. sampling : nt, sequence of ints, optional This parameter is only used in the case of the euclidean `metric` distance transform.

The sampling along each axis can be given by the `sampling` parameter which should be a sequence of length equal to the input rank, or a single number in which the `sampling` is assumed to be equal along all axes. return_distances : bool, optional The `return_distances` flag can be used to indicate if the distance transform is returned.

The default is True. return_indices : bool, optional The `return_indices` flags can be used to indicate if the feature transform is returned.

The default is False. distances : float64 ndarray, optional Optional output array to hold distances (if `return_distances` is True). indices : int64 ndarray, optional Optional output array to hold indices (if `return_indices` is True).

Returns ------- distances : ndarray Distance array if `return_distances` is True. indices : ndarray Indices array if `return_indices` is True.

Notes ----- This function employs a slow brute force algorithm, see also the function distance_transform_cdt for more efficient taxicab and chessboard algorithms.

val distance_transform_cdt : ?metric:[ `Chessboard | `Taxicab ] -> ?return_distances:Py.Object.t -> ?return_indices:Py.Object.t -> ?distances:Py.Object.t -> ?indices:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Distance transform for chamfer type of transforms.

Parameters ---------- input : array_like Input metric : 'chessboard', 'taxicab', optional The `metric` determines the type of chamfering that is done. If the `metric` is equal to 'taxicab' a structure is generated using generate_binary_structure with a squared distance equal to 1. If the `metric` is equal to 'chessboard', a `metric` is generated using generate_binary_structure with a squared distance equal to the dimensionality of the array. These choices correspond to the common interpretations of the 'taxicab' and the 'chessboard' distance metrics in two dimensions.

The default for `metric` is 'chessboard'. return_distances, return_indices : bool, optional The `return_distances`, and `return_indices` flags can be used to indicate if the distance transform, the feature transform, or both must be returned.

If the feature transform is returned (``return_indices=True``), the index of the closest background element is returned along the first axis of the result.

The `return_distances` default is True, and the `return_indices` default is False. distances, indices : ndarrays of int32, optional The `distances` and `indices` arguments can be used to give optional output arrays that must be the same shape as `input`.

val distance_transform_edt : ?sampling:[ `F of float | `I of int | `Sequence_of_same of Py.Object.t ] -> ?return_distances:bool -> ?return_indices:bool -> ?distances:[> `Ndarray ] Np.Obj.t -> ?indices:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Exact Euclidean distance transform.

In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element is returned along the first axis of the result.

Parameters ---------- input : array_like Input data to transform. Can be any type but will be converted into binary: 1 wherever input equates to True, 0 elsewhere. sampling : float or int, or sequence of same, optional Spacing of elements along each dimension. If a sequence, must be of length equal to the input rank; if a single number, this is used for all axes. If not specified, a grid spacing of unity is implied. return_distances : bool, optional Whether to return distance matrix. At least one of return_distances/return_indices must be True. Default is True. return_indices : bool, optional Whether to return indices matrix. Default is False. distances : ndarray, optional Used for output of distance array, must be of type float64. indices : ndarray, optional Used for output of indices, must be of type int32.

Returns ------- distance_transform_edt : ndarray or list of ndarrays Either distance matrix, index matrix, or a list of the two, depending on `return_x` flags and `distance` and `indices` input parameters.

Notes ----- The Euclidean distance transform gives values of the Euclidean distance::

n y_i = sqrt(sum (xi-bi)**2) i

where bi is the background point (value 0) with the smallest Euclidean distance to input points xi, and n is the number of dimensions.

Examples -------- >>> from scipy import ndimage >>> a = np.array((0,1,1,1,1, ... 0,0,1,1,1, ... 0,1,1,1,1, ... 0,1,1,1,0, ... 0,1,1,0,0)) >>> ndimage.distance_transform_edt(a) array([ 0. , 1. , 1.4142, 2.2361, 3. ], [ 0. , 0. , 1. , 2. , 2. ], [ 0. , 1. , 1.4142, 1.4142, 1. ], [ 0. , 1. , 1.4142, 1. , 0. ], [ 0. , 1. , 1. , 0. , 0. ])

With a sampling of 2 units along x, 1 along y:

>>> ndimage.distance_transform_edt(a, sampling=2,1) array([ 0. , 1. , 2. , 2.8284, 3.6056], [ 0. , 0. , 1. , 2. , 3. ], [ 0. , 1. , 2. , 2.2361, 2. ], [ 0. , 1. , 2. , 1. , 0. ], [ 0. , 1. , 1. , 0. , 0. ])

Asking for indices as well:

>>> edt, inds = ndimage.distance_transform_edt(a, return_indices=True) >>> inds array([[0, 0, 1, 1, 3], [1, 1, 1, 1, 3], [2, 2, 1, 3, 3], [3, 3, 4, 4, 3], [4, 4, 4, 4, 4]], [[0, 0, 1, 1, 4], [0, 1, 1, 1, 4], [0, 0, 1, 4, 4], [0, 0, 3, 3, 4], [0, 0, 3, 3, 4]])

With arrays provided for inplace outputs:

>>> indices = np.zeros(((np.ndim(a),) + a.shape), dtype=np.int32) >>> ndimage.distance_transform_edt(a, return_indices=True, indices=indices) array([ 0. , 1. , 1.4142, 2.2361, 3. ], [ 0. , 0. , 1. , 2. , 2. ], [ 0. , 1. , 1.4142, 1.4142, 1. ], [ 0. , 1. , 1.4142, 1. , 0. ], [ 0. , 1. , 1. , 0. , 0. ]) >>> indices array([[0, 0, 1, 1, 3], [1, 1, 1, 1, 3], [2, 2, 1, 3, 3], [3, 3, 4, 4, 3], [4, 4, 4, 4, 4]], [[0, 0, 1, 1, 4], [0, 1, 1, 1, 4], [0, 0, 1, 4, 4], [0, 0, 3, 3, 4], [0, 0, 3, 3, 4]])

val extrema : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[ `I of int | `Is of int list ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate the minimums and maximums of the values of an array at labels, along with their positions.

Parameters ---------- input : ndarray N-D image data to process. labels : ndarray, optional Labels of features in input. If not None, must be same shape as `input`. index : int or sequence of ints, optional Labels to include in output. If None (default), all values where non-zero `labels` are used.

Returns ------- minimums, maximums : int or ndarray Values of minimums and maximums in each feature. min_positions, max_positions : tuple or list of tuples Each tuple gives the N-D coordinates of the corresponding minimum or maximum.

See Also -------- maximum, minimum, maximum_position, minimum_position, center_of_mass

Examples -------- >>> a = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> from scipy import ndimage >>> ndimage.extrema(a) (0, 9, (0, 2), (3, 0))

Features to process can be specified using `labels` and `index`:

>>> lbl, nlbl = ndimage.label(a) >>> ndimage.extrema(a, lbl, index=np.arange(1, nlbl+1)) (array(1, 4, 3), array(5, 7, 9), (0, 0), (1, 3), (3, 1), (1, 0), (2, 3), (3, 0))

If no index is given, non-zero `labels` are processed:

>>> ndimage.extrema(a, lbl) (1, 9, (0, 0), (3, 0))

val find_objects : ?max_label:int -> input:Py.Object.t -> unit -> Py.Object.t

Find objects in a labeled array.

Parameters ---------- input : ndarray of ints Array containing objects defined by different labels. Labels with value 0 are ignored. max_label : int, optional Maximum label to be searched for in `input`. If max_label is not given, the positions of all objects are returned.

Returns ------- object_slices : list of tuples A list of tuples, with each tuple containing N slices (with N the dimension of the input array). Slices correspond to the minimal parallelepiped that contains the object. If a number is missing, None is returned instead of a slice.

See Also -------- label, center_of_mass

Notes ----- This function is very useful for isolating a volume of interest inside a 3-D array, that cannot be 'seen through'.

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((6,6), dtype=int) >>> a2:4, 2:4 = 1 >>> a4, 4 = 1 >>> a:2, :3 = 2 >>> a0, 5 = 3 >>> a array([2, 2, 2, 0, 0, 3], [2, 2, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0]) >>> ndimage.find_objects(a) (slice(2, 5, None), slice(2, 5, None)), (slice(0, 2, None), slice(0, 3, None)), (slice(0, 1, None), slice(5, 6, None)) >>> ndimage.find_objects(a, max_label=2) (slice(2, 5, None), slice(2, 5, None)), (slice(0, 2, None), slice(0, 3, None)) >>> ndimage.find_objects(a == 1, max_label=2) (slice(2, 5, None), slice(2, 5, None)), None

>>> loc = ndimage.find_objects(a)0 >>> aloc array([1, 1, 0], [1, 1, 0], [0, 0, 1])

val fourier_ellipsoid : ?n:int -> ?axis:int -> ?output:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> size:[ `F of float | `Sequence of Py.Object.t ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional ellipsoid Fourier filter.

The array is multiplied with the fourier transform of a ellipsoid of given sizes.

Parameters ---------- input : array_like The input array. size : float or sequence The size of the box used for filtering. If a float, `size` is the same for all axes. If a sequence, `size` has to contain one value for each axis. n : int, optional If `n` is negative (default), then the input is assumed to be the result of a complex fft. If `n` is larger than or equal to zero, the input is assumed to be the result of a real fft, and `n` gives the length of the array before transformation along the real transform direction. axis : int, optional The axis of the real transform. output : ndarray, optional If given, the result of filtering the input is placed in this array. None is returned in this case.

Returns ------- fourier_ellipsoid : ndarray The filtered input.

Notes ----- This function is implemented for arrays of rank 1, 2, or 3.

Examples -------- >>> from scipy import ndimage, misc >>> import numpy.fft >>> import matplotlib.pyplot as plt >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.ascent() >>> input_ = numpy.fft.fft2(ascent) >>> result = ndimage.fourier_ellipsoid(input_, size=20) >>> result = numpy.fft.ifft2(result) >>> ax1.imshow(ascent) >>> ax2.imshow(result.real) # the imaginary part is an artifact >>> plt.show()

val fourier_gaussian : ?n:int -> ?axis:int -> ?output:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> sigma:[ `F of float | `Sequence of Py.Object.t ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional Gaussian fourier filter.

The array is multiplied with the fourier transform of a Gaussian kernel.

Parameters ---------- input : array_like The input array. sigma : float or sequence The sigma of the Gaussian kernel. If a float, `sigma` is the same for all axes. If a sequence, `sigma` has to contain one value for each axis. n : int, optional If `n` is negative (default), then the input is assumed to be the result of a complex fft. If `n` is larger than or equal to zero, the input is assumed to be the result of a real fft, and `n` gives the length of the array before transformation along the real transform direction. axis : int, optional The axis of the real transform. output : ndarray, optional If given, the result of filtering the input is placed in this array. None is returned in this case.

Returns ------- fourier_gaussian : ndarray The filtered input.

Examples -------- >>> from scipy import ndimage, misc >>> import numpy.fft >>> import matplotlib.pyplot as plt >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.ascent() >>> input_ = numpy.fft.fft2(ascent) >>> result = ndimage.fourier_gaussian(input_, sigma=4) >>> result = numpy.fft.ifft2(result) >>> ax1.imshow(ascent) >>> ax2.imshow(result.real) # the imaginary part is an artifact >>> plt.show()

val fourier_shift : ?n:int -> ?axis:int -> ?output:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> shift:[ `F of float | `Sequence of Py.Object.t ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional Fourier shift filter.

The array is multiplied with the Fourier transform of a shift operation.

Parameters ---------- input : array_like The input array. shift : float or sequence The size of the box used for filtering. If a float, `shift` is the same for all axes. If a sequence, `shift` has to contain one value for each axis. n : int, optional If `n` is negative (default), then the input is assumed to be the result of a complex fft. If `n` is larger than or equal to zero, the input is assumed to be the result of a real fft, and `n` gives the length of the array before transformation along the real transform direction. axis : int, optional The axis of the real transform. output : ndarray, optional If given, the result of shifting the input is placed in this array. None is returned in this case.

Returns ------- fourier_shift : ndarray The shifted input.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> import numpy.fft >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.ascent() >>> input_ = numpy.fft.fft2(ascent) >>> result = ndimage.fourier_shift(input_, shift=200) >>> result = numpy.fft.ifft2(result) >>> ax1.imshow(ascent) >>> ax2.imshow(result.real) # the imaginary part is an artifact >>> plt.show()

val fourier_uniform : ?n:int -> ?axis:int -> ?output:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> size:[ `F of float | `Sequence of Py.Object.t ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional uniform fourier filter.

The array is multiplied with the Fourier transform of a box of given size.

Parameters ---------- input : array_like The input array. size : float or sequence The size of the box used for filtering. If a float, `size` is the same for all axes. If a sequence, `size` has to contain one value for each axis. n : int, optional If `n` is negative (default), then the input is assumed to be the result of a complex fft. If `n` is larger than or equal to zero, the input is assumed to be the result of a real fft, and `n` gives the length of the array before transformation along the real transform direction. axis : int, optional The axis of the real transform. output : ndarray, optional If given, the result of filtering the input is placed in this array. None is returned in this case.

Returns ------- fourier_uniform : ndarray The filtered input.

Examples -------- >>> from scipy import ndimage, misc >>> import numpy.fft >>> import matplotlib.pyplot as plt >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.ascent() >>> input_ = numpy.fft.fft2(ascent) >>> result = ndimage.fourier_uniform(input_, size=20) >>> result = numpy.fft.ifft2(result) >>> ax1.imshow(ascent) >>> ax2.imshow(result.real) # the imaginary part is an artifact >>> plt.show()

val gaussian_filter : ?order:[ `I of int | `Is of int list ] -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?truncate:float -> input:[> `Ndarray ] Np.Obj.t -> sigma: [ `Bool of bool | `F of float | `S of string | `Sequence_of_scalars of Py.Object.t | `I of int ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional Gaussian filter.

Parameters ---------- input : array_like The input array. sigma : scalar or sequence of scalars Standard deviation for Gaussian kernel. The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes. order : int or sequence of ints, optional The order of the filter along each axis is given as a sequence of integers, or as a single number. An order of 0 corresponds to convolution with a Gaussian kernel. A positive order corresponds to convolution with that derivative of a Gaussian. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. truncate : float Truncate the filter at this many standard deviations. Default is 4.0.

Returns ------- gaussian_filter : ndarray Returned array of same shape as `input`.

Notes ----- The multidimensional filter is implemented as a sequence of 1-D convolution filters. The intermediate arrays are stored in the same data type as the output. Therefore, for output types with a limited precision, the results may be imprecise because intermediate results may be stored with insufficient precision.

Examples -------- >>> from scipy.ndimage import gaussian_filter >>> a = np.arange(50, step=2).reshape((5,5)) >>> a array([ 0, 2, 4, 6, 8], [10, 12, 14, 16, 18], [20, 22, 24, 26, 28], [30, 32, 34, 36, 38], [40, 42, 44, 46, 48]) >>> gaussian_filter(a, sigma=1) array([ 4, 6, 8, 9, 11], [10, 12, 14, 15, 17], [20, 22, 24, 25, 27], [29, 31, 33, 34, 36], [35, 37, 39, 40, 42])

>>> from scipy import misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = gaussian_filter(ascent, sigma=5) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val gaussian_filter1d : ?axis:int -> ?order:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?truncate:float -> input:[> `Ndarray ] Np.Obj.t -> sigma:[ `F of float | `I of int | `Bool of bool | `S of string ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

1-D Gaussian filter.

Parameters ---------- input : array_like The input array. sigma : scalar standard deviation for Gaussian kernel axis : int, optional The axis of `input` along which to calculate. Default is -1. order : int, optional An order of 0 corresponds to convolution with a Gaussian kernel. A positive order corresponds to convolution with that derivative of a Gaussian. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. truncate : float, optional Truncate the filter at this many standard deviations. Default is 4.0.

Returns ------- gaussian_filter1d : ndarray

Examples -------- >>> from scipy.ndimage import gaussian_filter1d >>> gaussian_filter1d(1.0, 2.0, 3.0, 4.0, 5.0, 1) array( 1.42704095, 2.06782203, 3. , 3.93217797, 4.57295905) >>> gaussian_filter1d(1.0, 2.0, 3.0, 4.0, 5.0, 4) array( 2.91948343, 2.95023502, 3. , 3.04976498, 3.08051657) >>> import matplotlib.pyplot as plt >>> np.random.seed(280490) >>> x = np.random.randn(101).cumsum() >>> y3 = gaussian_filter1d(x, 3) >>> y6 = gaussian_filter1d(x, 6) >>> plt.plot(x, 'k', label='original data') >>> plt.plot(y3, '--', label='filtered, sigma=3') >>> plt.plot(y6, ':', label='filtered, sigma=6') >>> plt.legend() >>> plt.grid() >>> plt.show()

val gaussian_gradient_magnitude : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?kwargs:(string * Py.Object.t) list -> input:[> `Ndarray ] Np.Obj.t -> sigma: [ `Bool of bool | `F of float | `S of string | `Sequence_of_scalars of Py.Object.t | `I of int ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional gradient magnitude using Gaussian derivatives.

Parameters ---------- input : array_like The input array. sigma : scalar or sequence of scalars The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. Extra keyword arguments will be passed to gaussian_filter().

Returns ------- gaussian_gradient_magnitude : ndarray Filtered array. Has the same shape as `input`.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.gaussian_gradient_magnitude(ascent, sigma=5) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val gaussian_laplace : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?kwargs:(string * Py.Object.t) list -> input:[> `Ndarray ] Np.Obj.t -> sigma: [ `Bool of bool | `F of float | `S of string | `Sequence_of_scalars of Py.Object.t | `I of int ] -> unit -> Py.Object.t

Multidimensional Laplace filter using Gaussian second derivatives.

Parameters ---------- input : array_like The input array. sigma : scalar or sequence of scalars The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. Extra keyword arguments will be passed to gaussian_filter().

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> ascent = misc.ascent()

>>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side

>>> result = ndimage.gaussian_laplace(ascent, sigma=1) >>> ax1.imshow(result)

>>> result = ndimage.gaussian_laplace(ascent, sigma=3) >>> ax2.imshow(result) >>> plt.show()

val generate_binary_structure : rank:int -> connectivity:int -> unit -> Py.Object.t

Generate a binary structure for binary morphological operations.

Parameters ---------- rank : int Number of dimensions of the array to which the structuring element will be applied, as returned by `np.ndim`. connectivity : int `connectivity` determines which elements of the output array belong to the structure, i.e., are considered as neighbors of the central element. Elements up to a squared distance of `connectivity` from the center are considered neighbors. `connectivity` may range from 1 (no diagonal elements are neighbors) to `rank` (all elements are neighbors).

Returns ------- output : ndarray of bools Structuring element which may be used for binary morphological operations, with `rank` dimensions and all dimensions equal to 3.

See also -------- iterate_structure, binary_dilation, binary_erosion

Notes ----- `generate_binary_structure` can only create structuring elements with dimensions equal to 3, i.e., minimal dimensions. For larger structuring elements, that are useful e.g., for eroding large objects, one may either use `iterate_structure`, or create directly custom arrays with numpy functions such as `numpy.ones`.

Examples -------- >>> from scipy import ndimage >>> struct = ndimage.generate_binary_structure(2, 1) >>> struct array([False, True, False], [ True, True, True], [False, True, False], dtype=bool) >>> a = np.zeros((5,5)) >>> a2, 2 = 1 >>> a array([ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 1., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.]) >>> b = ndimage.binary_dilation(a, structure=struct).astype(a.dtype) >>> b array([ 0., 0., 0., 0., 0.], [ 0., 0., 1., 0., 0.], [ 0., 1., 1., 1., 0.], [ 0., 0., 1., 0., 0.], [ 0., 0., 0., 0., 0.]) >>> ndimage.binary_dilation(b, structure=struct).astype(a.dtype) array([ 0., 0., 1., 0., 0.], [ 0., 1., 1., 1., 0.], [ 1., 1., 1., 1., 1.], [ 0., 1., 1., 1., 0.], [ 0., 0., 1., 0., 0.]) >>> struct = ndimage.generate_binary_structure(2, 2) >>> struct array([ True, True, True], [ True, True, True], [ True, True, True], dtype=bool) >>> struct = ndimage.generate_binary_structure(3, 1) >>> struct # no diagonal elements array([[False, False, False], [False, True, False], [False, False, False]], [[False, True, False], [ True, True, True], [False, True, False]], [[False, False, False], [False, True, False], [False, False, False]], dtype=bool)

val generic_filter : ?size: [ `Bool of bool | `F of float | `S of string | `Tuple of Py.Object.t | `I of int ] -> ?footprint:[> `Ndarray ] Np.Obj.t -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> ?extra_arguments:Py.Object.t -> ?extra_keywords:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> function_: [ `Scipy_LowLevelCallable of Py.Object.t | `Callable of Py.Object.t ] -> unit -> Py.Object.t

Calculate a multidimensional filter using the given function.

At each element the provided function is called. The input values within the filter footprint at that element are passed to the function as a 1-D array of double values.

Parameters ---------- input : array_like The input array. function : callable, scipy.LowLevelCallable Function to apply at each element. size : scalar or tuple, optional See footprint, below. Ignored if footprint is given. footprint : array, optional Either `size` or `footprint` must be defined. `size` gives the shape that is taken from the input array, at every element position, to define the input to the filter function. `footprint` is a boolean array that specifies (implicitly) a shape, but also which of the elements within this shape will get passed to the filter function. Thus ``size=(n,m)`` is equivalent to ``footprint=np.ones((n,m))``. We adjust `size` to the number of dimensions of the input array, so that, if the input array is shape (10,10,10), and `size` is 2, then the actual size used is (2,2,2). When `footprint` is given, `size` is ignored. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis. extra_arguments : sequence, optional Sequence of extra positional arguments to pass to passed function. extra_keywords : dict, optional dict of extra keyword arguments to pass to passed function.

Notes ----- This function also accepts low-level callback functions with one of the following signatures and wrapped in `scipy.LowLevelCallable`:

.. code:: c

int callback(double *buffer, npy_intp filter_size, double *return_value, void *user_data) int callback(double *buffer, intptr_t filter_size, double *return_value, void *user_data)

The calling function iterates over the elements of the input and output arrays, calling the callback function at each element. The elements within the footprint of the filter at the current element are passed through the ``buffer`` parameter, and the number of elements within the footprint through ``filter_size``. The calculated value is returned in ``return_value``. ``user_data`` is the data pointer provided to `scipy.LowLevelCallable` as-is.

The callback function must return an integer error status that is zero if something went wrong and one otherwise. If an error occurs, you should normally set the python error status with an informative message before returning, otherwise a default error message is set by the calling function.

In addition, some other low-level function pointer specifications are accepted, but these are for backward compatibility only and should not be used in new code.

val generic_filter1d : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:int -> ?extra_arguments:Py.Object.t -> ?extra_keywords:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> function_: [ `Scipy_LowLevelCallable of Py.Object.t | `Callable of Py.Object.t ] -> filter_size:[ `F of float | `I of int | `Bool of bool | `S of string ] -> unit -> Py.Object.t

Calculate a 1-D filter along the given axis.

`generic_filter1d` iterates over the lines of the array, calling the given function at each line. The arguments of the line are the input line, and the output line. The input and output lines are 1-D double arrays. The input line is extended appropriately according to the filter size and origin. The output line must be modified in-place with the result.

Parameters ---------- input : array_like The input array. function : callable, scipy.LowLevelCallable Function to apply along given axis. filter_size : scalar Length of the filter. axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. extra_arguments : sequence, optional Sequence of extra positional arguments to pass to passed function. extra_keywords : dict, optional dict of extra keyword arguments to pass to passed function.

Notes ----- This function also accepts low-level callback functions with one of the following signatures and wrapped in `scipy.LowLevelCallable`:

.. code:: c

int function(double *input_line, npy_intp input_length, double *output_line, npy_intp output_length, void *user_data) int function(double *input_line, intptr_t input_length, double *output_line, intptr_t output_length, void *user_data)

The calling function iterates over the lines of the input and output arrays, calling the callback function at each line. The current line is extended according to the border conditions set by the calling function, and the result is copied into the array that is passed through ``input_line``. The length of the input line (after extension) is passed through ``input_length``. The callback function should apply the filter and store the result in the array passed through ``output_line``. The length of the output line is passed through ``output_length``. ``user_data`` is the data pointer provided to `scipy.LowLevelCallable` as-is.

The callback function must return an integer error status that is zero if something went wrong and one otherwise. If an error occurs, you should normally set the python error status with an informative message before returning, otherwise a default error message is set by the calling function.

In addition, some other low-level function pointer specifications are accepted, but these are for backward compatibility only and should not be used in new code.

val generic_gradient_magnitude : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?extra_arguments:Py.Object.t -> ?extra_keywords:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> derivative:Py.Object.t -> unit -> Py.Object.t

Gradient magnitude using a provided gradient function.

Parameters ---------- input : array_like The input array. derivative : callable Callable with the following signature::

derivative(input, axis, output, mode, cval, *extra_arguments, **extra_keywords)

See `extra_arguments`, `extra_keywords` below. `derivative` can assume that `input` and `output` are ndarrays. Note that the output from `derivative` is modified inplace; be careful to copy important inputs before returning them. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. extra_keywords : dict, optional dict of extra keyword arguments to pass to passed function. extra_arguments : sequence, optional Sequence of extra positional arguments to pass to passed function.

val generic_laplace : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?extra_arguments:Py.Object.t -> ?extra_keywords:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> derivative2:Py.Object.t -> unit -> Py.Object.t

N-D Laplace filter using a provided second derivative function.

Parameters ---------- input : array_like The input array. derivative2 : callable Callable with the following signature::

derivative2(input, axis, output, mode, cval, *extra_arguments, **extra_keywords)

See `extra_arguments`, `extra_keywords` below. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. extra_keywords : dict, optional dict of extra keyword arguments to pass to passed function. extra_arguments : sequence, optional Sequence of extra positional arguments to pass to passed function.

val geometric_transform : ?output_shape:int list -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?order:int -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?prefilter:bool -> ?extra_arguments:Py.Object.t -> ?extra_keywords:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> mapping:[ `Scipy_LowLevelCallable of Py.Object.t | `Callable of Py.Object.t ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Apply an arbitrary geometric transform.

The given mapping function is used to find, for each point in the output, the corresponding coordinates in the input. The value of the input at those coordinates is determined by spline interpolation of the requested order.

Parameters ---------- input : array_like The input array. mapping : callable, scipy.LowLevelCallable A callable object that accepts a tuple of length equal to the output array rank, and returns the corresponding input coordinates as a tuple of length equal to the input array rank. output_shape : tuple of ints, optional Shape tuple. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with `spline_filter` before interpolation. The default is True, which will create a temporary `float64` array of filtered values if `order > 1`. If setting this to False, the output will be slightly blurred if `order > 1`, unless the input is prefiltered, i.e. it is the result of calling `spline_filter` on the original input. extra_arguments : tuple, optional Extra arguments passed to `mapping`. extra_keywords : dict, optional Extra keywords passed to `mapping`.

Returns ------- output : ndarray The filtered input.

See Also -------- map_coordinates, affine_transform, spline_filter1d

Notes ----- This function also accepts low-level callback functions with one the following signatures and wrapped in `scipy.LowLevelCallable`:

.. code:: c

int mapping(npy_intp *output_coordinates, double *input_coordinates, int output_rank, int input_rank, void *user_data) int mapping(intptr_t *output_coordinates, double *input_coordinates, int output_rank, int input_rank, void *user_data)

The calling function iterates over the elements of the output array, calling the callback function at each element. The coordinates of the current output element are passed through ``output_coordinates``. The callback function must return the coordinates at which the input must be interpolated in ``input_coordinates``. The rank of the input and output arrays are given by ``input_rank`` and ``output_rank`` respectively. ``user_data`` is the data pointer provided to `scipy.LowLevelCallable` as-is.

The callback function must return an integer error status that is zero if something went wrong and one otherwise. If an error occurs, you should normally set the Python error status with an informative message before returning, otherwise a default error message is set by the calling function.

In addition, some other low-level function pointer specifications are accepted, but these are for backward compatibility only and should not be used in new code.

Examples -------- >>> import numpy as np >>> from scipy.ndimage import geometric_transform >>> a = np.arange(12.).reshape((4, 3)) >>> def shift_func(output_coords): ... return (output_coords0 - 0.5, output_coords1 - 0.5) ... >>> geometric_transform(a, shift_func) array([ 0. , 0. , 0. ], [ 0. , 1.362, 2.738], [ 0. , 4.812, 6.187], [ 0. , 8.263, 9.637])

>>> b = 1, 2, 3, 4, 5 >>> def shift_func(output_coords): ... return (output_coords0 - 3,) ... >>> geometric_transform(b, shift_func, mode='constant') array(0, 0, 0, 1, 2) >>> geometric_transform(b, shift_func, mode='nearest') array(1, 1, 1, 1, 2) >>> geometric_transform(b, shift_func, mode='reflect') array(3, 2, 1, 1, 2) >>> geometric_transform(b, shift_func, mode='wrap') array(2, 3, 4, 1, 2)

val grey_closing : ?size:int list -> ?footprint:Py.Object.t -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional grayscale closing.

A grayscale closing consists in the succession of a grayscale dilation, and a grayscale erosion.

Parameters ---------- input : array_like Array over which the grayscale closing is to be computed. size : tuple of ints Shape of a flat and full structuring element used for the grayscale closing. Optional if `footprint` or `structure` is provided. footprint : array of ints, optional Positions of non-infinite elements of a flat structuring element used for the grayscale closing. structure : array of ints, optional Structuring element used for the grayscale closing. `structure` may be a non-flat structuring element. output : array, optional An array used for storing the output of the closing may be provided. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the array borders are handled, where `cval` is the value when mode is equal to 'constant'. Default is 'reflect' cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : scalar, optional The `origin` parameter controls the placement of the filter. Default 0

Returns ------- grey_closing : ndarray Result of the grayscale closing of `input` with `structure`.

See also -------- binary_closing, grey_dilation, grey_erosion, grey_opening, generate_binary_structure

Notes ----- The action of a grayscale closing with a flat structuring element amounts to smoothen deep local minima, whereas binary closing fills small holes.

References ---------- .. 1 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.arange(36).reshape((6,6)) >>> a3,3 = 0 >>> a array([ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 0, 22, 23], [24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35]) >>> ndimage.grey_closing(a, size=(3,3)) array([ 7, 7, 8, 9, 10, 11], [ 7, 7, 8, 9, 10, 11], [13, 13, 14, 15, 16, 17], [19, 19, 20, 20, 22, 23], [25, 25, 26, 27, 28, 29], [31, 31, 32, 33, 34, 35]) >>> # Note that the local minimum a3,3 has disappeared

val grey_dilation : ?size:int list -> ?footprint:Py.Object.t -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a greyscale dilation, using either a structuring element, or a footprint corresponding to a flat structuring element.

Grayscale dilation is a mathematical morphology operation. For the simple case of a full and flat structuring element, it can be viewed as a maximum filter over a sliding window.

Parameters ---------- input : array_like Array over which the grayscale dilation is to be computed. size : tuple of ints Shape of a flat and full structuring element used for the grayscale dilation. Optional if `footprint` or `structure` is provided. footprint : array of ints, optional Positions of non-infinite elements of a flat structuring element used for the grayscale dilation. Non-zero values give the set of neighbors of the center over which the maximum is chosen. structure : array of ints, optional Structuring element used for the grayscale dilation. `structure` may be a non-flat structuring element. output : array, optional An array used for storing the output of the dilation may be provided. mode : 'reflect','constant','nearest','mirror', 'wrap', optional The `mode` parameter determines how the array borders are handled, where `cval` is the value when mode is equal to 'constant'. Default is 'reflect' cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : scalar, optional The `origin` parameter controls the placement of the filter. Default 0

Returns ------- grey_dilation : ndarray Grayscale dilation of `input`.

See also -------- binary_dilation, grey_erosion, grey_closing, grey_opening generate_binary_structure, maximum_filter

Notes ----- The grayscale dilation of an image input by a structuring element s defined over a domain E is given by:

(input+s)(x) = max nput(y) + s(x-y), for y in E

In particular, for structuring elements defined as s(y) = 0 for y in E, the grayscale dilation computes the maximum of the input image inside a sliding window defined by E.

Grayscale dilation 1_ is a *mathematical morphology* operation 2_.

References ---------- .. 1 https://en.wikipedia.org/wiki/Dilation_%28morphology%29 .. 2 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((7,7), dtype=int) >>> a2:5, 2:5 = 1 >>> a4,4 = 2; a2,3 = 3 >>> a array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> ndimage.grey_dilation(a, size=(3,3)) array([0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 3, 3, 1, 0], [0, 1, 3, 3, 3, 1, 0], [0, 1, 3, 3, 3, 2, 0], [0, 1, 1, 2, 2, 2, 0], [0, 1, 1, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0]) >>> ndimage.grey_dilation(a, footprint=np.ones((3,3))) array([0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 3, 3, 1, 0], [0, 1, 3, 3, 3, 1, 0], [0, 1, 3, 3, 3, 2, 0], [0, 1, 1, 2, 2, 2, 0], [0, 1, 1, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0]) >>> s = ndimage.generate_binary_structure(2,1) >>> s array([False, True, False], [ True, True, True], [False, True, False], dtype=bool) >>> ndimage.grey_dilation(a, footprint=s) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0], [0, 1, 3, 3, 3, 1, 0], [0, 1, 1, 3, 2, 1, 0], [0, 1, 1, 2, 2, 2, 0], [0, 0, 1, 1, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> ndimage.grey_dilation(a, size=(3,3), structure=np.ones((3,3))) array([1, 1, 1, 1, 1, 1, 1], [1, 2, 4, 4, 4, 2, 1], [1, 2, 4, 4, 4, 2, 1], [1, 2, 4, 4, 4, 3, 1], [1, 2, 2, 3, 3, 3, 1], [1, 2, 2, 3, 3, 3, 1], [1, 1, 1, 1, 1, 1, 1])

val grey_erosion : ?size:int list -> ?footprint:Py.Object.t -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a greyscale erosion, using either a structuring element, or a footprint corresponding to a flat structuring element.

Grayscale erosion is a mathematical morphology operation. For the simple case of a full and flat structuring element, it can be viewed as a minimum filter over a sliding window.

Parameters ---------- input : array_like Array over which the grayscale erosion is to be computed. size : tuple of ints Shape of a flat and full structuring element used for the grayscale erosion. Optional if `footprint` or `structure` is provided. footprint : array of ints, optional Positions of non-infinite elements of a flat structuring element used for the grayscale erosion. Non-zero values give the set of neighbors of the center over which the minimum is chosen. structure : array of ints, optional Structuring element used for the grayscale erosion. `structure` may be a non-flat structuring element. output : array, optional An array used for storing the output of the erosion may be provided. mode : 'reflect','constant','nearest','mirror', 'wrap', optional The `mode` parameter determines how the array borders are handled, where `cval` is the value when mode is equal to 'constant'. Default is 'reflect' cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : scalar, optional The `origin` parameter controls the placement of the filter. Default 0

Returns ------- output : ndarray Grayscale erosion of `input`.

See also -------- binary_erosion, grey_dilation, grey_opening, grey_closing generate_binary_structure, minimum_filter

Notes ----- The grayscale erosion of an image input by a structuring element s defined over a domain E is given by:

(input+s)(x) = min nput(y) - s(x-y), for y in E

In particular, for structuring elements defined as s(y) = 0 for y in E, the grayscale erosion computes the minimum of the input image inside a sliding window defined by E.

Grayscale erosion 1_ is a *mathematical morphology* operation 2_.

References ---------- .. 1 https://en.wikipedia.org/wiki/Erosion_%28morphology%29 .. 2 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((7,7), dtype=int) >>> a1:6, 1:6 = 3 >>> a4,4 = 2; a2,3 = 1 >>> a array([0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0], [0, 3, 3, 1, 3, 3, 0], [0, 3, 3, 3, 3, 3, 0], [0, 3, 3, 3, 2, 3, 0], [0, 3, 3, 3, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0]) >>> ndimage.grey_erosion(a, size=(3,3)) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 3, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> footprint = ndimage.generate_binary_structure(2, 1) >>> footprint array([False, True, False], [ True, True, True], [False, True, False], dtype=bool) >>> # Diagonally-connected elements are not considered neighbors >>> ndimage.grey_erosion(a, size=(3,3), footprint=footprint) array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 3, 1, 2, 0, 0], [0, 0, 3, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0])

val grey_opening : ?size:int list -> ?footprint:Py.Object.t -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional grayscale opening.

A grayscale opening consists in the succession of a grayscale erosion, and a grayscale dilation.

Parameters ---------- input : array_like Array over which the grayscale opening is to be computed. size : tuple of ints Shape of a flat and full structuring element used for the grayscale opening. Optional if `footprint` or `structure` is provided. footprint : array of ints, optional Positions of non-infinite elements of a flat structuring element used for the grayscale opening. structure : array of ints, optional Structuring element used for the grayscale opening. `structure` may be a non-flat structuring element. output : array, optional An array used for storing the output of the opening may be provided. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the array borders are handled, where `cval` is the value when mode is equal to 'constant'. Default is 'reflect' cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : scalar, optional The `origin` parameter controls the placement of the filter. Default 0

Returns ------- grey_opening : ndarray Result of the grayscale opening of `input` with `structure`.

See also -------- binary_opening, grey_dilation, grey_erosion, grey_closing generate_binary_structure

Notes ----- The action of a grayscale opening with a flat structuring element amounts to smoothen high local maxima, whereas binary opening erases small objects.

References ---------- .. 1 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.arange(36).reshape((6,6)) >>> a3, 3 = 50 >>> a array([ 0, 1, 2, 3, 4, 5], [ 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 50, 22, 23], [24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35]) >>> ndimage.grey_opening(a, size=(3,3)) array([ 0, 1, 2, 3, 4, 4], [ 6, 7, 8, 9, 10, 10], [12, 13, 14, 15, 16, 16], [18, 19, 20, 22, 22, 22], [24, 25, 26, 27, 28, 28], [24, 25, 26, 27, 28, 28]) >>> # Note that the local maximum a3,3 has disappeared

val histogram : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[ `I of int | `Is of int list ] -> input:[> `Ndarray ] Np.Obj.t -> min:Py.Object.t -> max:Py.Object.t -> bins:int -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate the histogram of the values of an array, optionally at labels.

Histogram calculates the frequency of values in an array within bins determined by `min`, `max`, and `bins`. The `labels` and `index` keywords can limit the scope of the histogram to specified sub-regions within the array.

Parameters ---------- input : array_like Data for which to calculate histogram. min, max : int Minimum and maximum values of range of histogram bins. bins : int Number of bins. labels : array_like, optional Labels for objects in `input`. If not None, must be same shape as `input`. index : int or sequence of ints, optional Label or labels for which to calculate histogram. If None, all values where label is greater than zero are used

Returns ------- hist : ndarray Histogram counts.

Examples -------- >>> a = np.array([ 0. , 0.2146, 0.5962, 0. ], ... [ 0. , 0.7778, 0. , 0. ], ... [ 0. , 0. , 0. , 0. ], ... [ 0. , 0. , 0.7181, 0.2787], ... [ 0. , 0. , 0.6573, 0.3094]) >>> from scipy import ndimage >>> ndimage.measurements.histogram(a, 0, 1, 10) array(13, 0, 2, 1, 0, 1, 1, 2, 0, 0)

With labels and no indices, non-zero elements are counted:

>>> lbl, nlbl = ndimage.label(a) >>> ndimage.measurements.histogram(a, 0, 1, 10, lbl) array(0, 0, 2, 1, 0, 1, 1, 2, 0, 0)

Indices can be used to count only certain objects:

>>> ndimage.measurements.histogram(a, 0, 1, 10, lbl, 2) array(0, 0, 1, 1, 0, 0, 1, 1, 0, 0)

val iterate_structure : ?origin:Py.Object.t -> structure:[> `Ndarray ] Np.Obj.t -> iterations:int -> unit -> Py.Object.t

Iterate a structure by dilating it with itself.

Parameters ---------- structure : array_like Structuring element (an array of bools, for example), to be dilated with itself. iterations : int number of dilations performed on the structure with itself origin : optional If origin is None, only the iterated structure is returned. If not, a tuple of the iterated structure and the modified origin is returned.

Returns ------- iterate_structure : ndarray of bools A new structuring element obtained by dilating `structure` (`iterations` - 1) times with itself.

See also -------- generate_binary_structure

Examples -------- >>> from scipy import ndimage >>> struct = ndimage.generate_binary_structure(2, 1) >>> struct.astype(int) array([0, 1, 0], [1, 1, 1], [0, 1, 0]) >>> ndimage.iterate_structure(struct, 2).astype(int) array([0, 0, 1, 0, 0], [0, 1, 1, 1, 0], [1, 1, 1, 1, 1], [0, 1, 1, 1, 0], [0, 0, 1, 0, 0]) >>> ndimage.iterate_structure(struct, 3).astype(int) array([0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1], [0, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0])

val label : ?structure:[> `Ndarray ] Np.Obj.t -> ?output:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t * int

Label features in an array.

Parameters ---------- input : array_like An array-like object to be labeled. Any non-zero values in `input` are counted as features and zero values are considered the background. structure : array_like, optional A structuring element that defines feature connections. `structure` must be centrosymmetric (see Notes). If no structuring element is provided, one is automatically generated with a squared connectivity equal to one. That is, for a 2-D `input` array, the default structuring element is::

[0,1,0], [1,1,1], [0,1,0]

output : (None, data-type, array_like), optional If `output` is a data type, it specifies the type of the resulting labeled feature array. If `output` is an array-like object, then `output` will be updated with the labeled features from this function. This function can operate in-place, by passing output=input. Note that the output must be able to store the largest label, or this function will raise an Exception.

Returns ------- label : ndarray or int An integer ndarray where each unique feature in `input` has a unique label in the returned array. num_features : int How many objects were found.

If `output` is None, this function returns a tuple of (`labeled_array`, `num_features`).

If `output` is a ndarray, then it will be updated with values in `labeled_array` and only `num_features` will be returned by this function.

See Also -------- find_objects : generate a list of slices for the labeled features (or objects); useful for finding features' position or dimensions

Notes ----- A centrosymmetric matrix is a matrix that is symmetric about the center. See 1_ for more information.

The `structure` matrix must be centrosymmetric to ensure two-way connections. For instance, if the `structure` matrix is not centrosymmetric and is defined as::

[0,1,0], [1,1,0], [0,0,0]

and the `input` is::

[1,2], [0,3]

then the structure matrix would indicate the entry 2 in the input is connected to 1, but 1 is not connected to 2.

Examples -------- Create an image with some features, then label it using the default (cross-shaped) structuring element:

>>> from scipy.ndimage import label, generate_binary_structure >>> a = np.array([0,0,1,1,0,0], ... [0,0,0,1,0,0], ... [1,1,0,0,1,0], ... [0,0,0,1,0,0]) >>> labeled_array, num_features = label(a)

Each of the 4 features are labeled with a different integer:

>>> num_features 4 >>> labeled_array array([0, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0], [2, 2, 0, 0, 3, 0], [0, 0, 0, 4, 0, 0])

Generate a structuring element that will consider features connected even if they touch diagonally:

>>> s = generate_binary_structure(2,2)

or,

>>> s = [1,1,1], ... [1,1,1], ... [1,1,1]

Label the image using the new structuring element:

>>> labeled_array, num_features = label(a, structure=s)

Show the 2 labeled features (note that features 1, 3, and 4 from above are now considered a single feature):

>>> num_features 2 >>> labeled_array array([0, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0], [2, 2, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0])

References ----------

.. 1 James R. Weaver, 'Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors.' The American Mathematical Monthly 92.10 (1985): 711-717.

val labeled_comprehension : ?pass_positions:bool -> input:[> `Ndarray ] Np.Obj.t -> labels:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `None ] -> index:[ `I of int | `Is of int list | `None ] -> func:Py.Object.t -> out_dtype:Np.Dtype.t -> default:[ `F of float | `I of int | `None ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Roughly equivalent to func(input[labels == i]) for i in index.

Sequentially applies an arbitrary function (that works on array_like input) to subsets of an N-D image array specified by `labels` and `index`. The option exists to provide the function with positional parameters as the second argument.

Parameters ---------- input : array_like Data from which to select `labels` to process. labels : array_like or None Labels to objects in `input`. If not None, array must be same shape as `input`. If None, `func` is applied to raveled `input`. index : int, sequence of ints or None Subset of `labels` to which to apply `func`. If a scalar, a single value is returned. If None, `func` is applied to all non-zero values of `labels`. func : callable Python function to apply to `labels` from `input`. out_dtype : dtype Dtype to use for `result`. default : int, float or None Default return value when a element of `index` does not exist in `labels`. pass_positions : bool, optional If True, pass linear indices to `func` as a second argument. Default is False.

Returns ------- result : ndarray Result of applying `func` to each of `labels` to `input` in `index`.

Examples -------- >>> a = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> from scipy import ndimage >>> lbl, nlbl = ndimage.label(a) >>> lbls = np.arange(1, nlbl+1) >>> ndimage.labeled_comprehension(a, lbl, lbls, np.mean, float, 0) array( 2.75, 5.5 , 6. )

Falling back to `default`:

>>> lbls = np.arange(1, nlbl+2) >>> ndimage.labeled_comprehension(a, lbl, lbls, np.mean, float, -1) array( 2.75, 5.5 , 6. , -1. )

Passing positions:

>>> def fn(val, pos): ... print('fn says: %s : %s' % (val, pos)) ... return (val.sum()) if (pos.sum() % 2 == 0) else (-val.sum()) ... >>> ndimage.labeled_comprehension(a, lbl, lbls, fn, float, 0, True) fn says: 1 2 5 3 : 0 1 4 5 fn says: 4 7 : 7 11 fn says: 9 3 : 12 13 array( 11., 11., -12., 0.)

val laplace : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

N-D Laplace filter based on approximate second derivatives.

Parameters ---------- input : array_like The input array. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.laplace(ascent) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val map_coordinates : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?order:int -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?prefilter:bool -> input:[> `Ndarray ] Np.Obj.t -> coordinates:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Map the input array to new coordinates by interpolation.

The array of coordinates is used to find, for each point in the output, the corresponding coordinates in the input. The value of the input at those coordinates is determined by spline interpolation of the requested order.

The shape of the output is derived from that of the coordinate array by dropping the first axis. The values of the array along the first axis are the coordinates in the input array at which the output value is found.

Parameters ---------- input : array_like The input array. coordinates : array_like The coordinates at which `input` is evaluated. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with `spline_filter` before interpolation. The default is True, which will create a temporary `float64` array of filtered values if `order > 1`. If setting this to False, the output will be slightly blurred if `order > 1`, unless the input is prefiltered, i.e. it is the result of calling `spline_filter` on the original input.

Returns ------- map_coordinates : ndarray The result of transforming the input. The shape of the output is derived from that of `coordinates` by dropping the first axis.

See Also -------- spline_filter, geometric_transform, scipy.interpolate

Examples -------- >>> from scipy import ndimage >>> a = np.arange(12.).reshape((4, 3)) >>> a array([ 0., 1., 2.], [ 3., 4., 5.], [ 6., 7., 8.], [ 9., 10., 11.]) >>> ndimage.map_coordinates(a, [0.5, 2], [0.5, 1], order=1) array( 2., 7.)

Above, the interpolated value of a0.5, 0.5 gives output0, while a2, 1 is output1.

>>> inds = np.array([0.5, 2], [0.5, 4]) >>> ndimage.map_coordinates(a, inds, order=1, cval=-33.3) array( 2. , -33.3) >>> ndimage.map_coordinates(a, inds, order=1, mode='nearest') array( 2., 8.) >>> ndimage.map_coordinates(a, inds, order=1, cval=0, output=bool) array( True, False, dtype=bool)

val maximum : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate the maximum of the values of an array over labeled regions.

Parameters ---------- input : array_like Array_like of values. For each region specified by `labels`, the maximal values of `input` over the region is computed. labels : array_like, optional An array of integers marking different regions over which the maximum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the maximum over the whole array is returned. index : array_like, optional A list of region labels that are taken into account for computing the maxima. If index is None, the maximum over all elements where `labels` is non-zero is returned.

Returns ------- output : float or list of floats List of maxima of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a float is returned: the maximal value of `input` if `labels` is None, and the maximal value of elements where `labels` is greater than zero if `index` is None.

See also -------- label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation

Notes ----- The function returns a Python list and not a NumPy array, use `np.array` to convert the list to an array.

Examples -------- >>> a = np.arange(16).reshape((4,4)) >>> a array([ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]) >>> labels = np.zeros_like(a) >>> labels:2,:2 = 1 >>> labels2:, 1:3 = 2 >>> labels array([1, 1, 0, 0], [1, 1, 0, 0], [0, 2, 2, 0], [0, 2, 2, 0]) >>> from scipy import ndimage >>> ndimage.maximum(a) 15.0 >>> ndimage.maximum(a, labels=labels, index=1,2) 5.0, 14.0 >>> ndimage.maximum(a, labels=labels) 14.0

>>> b = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> labels, labels_nb = ndimage.label(b) >>> labels array([1, 1, 0, 0], [1, 1, 0, 2], [0, 0, 0, 2], [3, 3, 0, 0]) >>> ndimage.maximum(b, labels=labels, index=np.arange(1, labels_nb + 1)) 5.0, 7.0, 9.0

val maximum_filter : ?size: [ `Bool of bool | `F of float | `S of string | `Tuple of Py.Object.t | `I of int ] -> ?footprint:[> `Ndarray ] Np.Obj.t -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a multidimensional maximum filter.

Parameters ---------- input : array_like The input array. size : scalar or tuple, optional See footprint, below. Ignored if footprint is given. footprint : array, optional Either `size` or `footprint` must be defined. `size` gives the shape that is taken from the input array, at every element position, to define the input to the filter function. `footprint` is a boolean array that specifies (implicitly) a shape, but also which of the elements within this shape will get passed to the filter function. Thus ``size=(n,m)`` is equivalent to ``footprint=np.ones((n,m))``. We adjust `size` to the number of dimensions of the input array, so that, if the input array is shape (10,10,10), and `size` is 2, then the actual size used is (2,2,2). When `footprint` is given, `size` is ignored. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- maximum_filter : ndarray Filtered array. Has the same shape as `input`.

Notes ----- A sequence of modes (one per axis) is only supported when the footprint is separable. Otherwise, a single mode string must be provided.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.maximum_filter(ascent, size=20) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val maximum_filter1d : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:int -> input:[> `Ndarray ] Np.Obj.t -> size:int -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t option

Calculate a 1-D maximum filter along the given axis.

The lines of the array along the given axis are filtered with a maximum filter of given size.

Parameters ---------- input : array_like The input array. size : int Length along which to calculate the 1-D maximum. axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right.

Returns ------- maximum1d : ndarray, None Maximum-filtered array with same shape as input. None if `output` is not None

Notes ----- This function implements the MAXLIST algorithm 1_, as described by Richard Harter 2_, and has a guaranteed O(n) performance, `n` being the `input` length, regardless of filter size.

References ---------- .. 1 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.2777 .. 2 http://www.richardhartersworld.com/cri/2001/slidingmin.html

Examples -------- >>> from scipy.ndimage import maximum_filter1d >>> maximum_filter1d(2, 8, 0, 4, 1, 9, 9, 0, size=3) array(8, 8, 8, 4, 9, 9, 9, 9)

val maximum_position : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Find the positions of the maximums of the values of an array at labels.

For each region specified by `labels`, the position of the maximum value of `input` within the region is returned.

Parameters ---------- input : array_like Array_like of values. labels : array_like, optional An array of integers marking different regions over which the position of the maximum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the location of the first maximum over the whole array is returned.

The `labels` argument only works when `index` is specified. index : array_like, optional A list of region labels that are taken into account for finding the location of the maxima. If `index` is None, the first maximum over all elements where `labels` is non-zero is returned.

The `index` argument only works when `labels` is specified.

Returns ------- output : list of tuples of ints List of tuples of ints that specify the location of maxima of `input` over the regions determined by `labels` and whose index is in `index`.

If `index` or `labels` are not specified, a tuple of ints is returned specifying the location of the ``first`` maximal value of `input`.

See also -------- label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation

Examples -------- >>> from scipy import ndimage >>> a = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> ndimage.maximum_position(a) (3, 0)

Features to process can be specified using `labels` and `index`:

>>> lbl = np.array([0, 1, 2, 3], ... [0, 1, 2, 3], ... [0, 1, 2, 3], ... [0, 1, 2, 3]) >>> ndimage.maximum_position(a, lbl, 1) (1, 1)

If no index is given, non-zero `labels` are processed:

>>> ndimage.maximum_position(a, lbl) (2, 3)

If there are no maxima, the position of the first element is returned:

>>> ndimage.maximum_position(a, lbl, 2) (0, 2)

val mean : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[ `I of int | `Is of int list ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate the mean of the values of an array at labels.

Parameters ---------- input : array_like Array on which to compute the mean of elements over distinct regions. labels : array_like, optional Array of labels of same shape, or broadcastable to the same shape as `input`. All elements sharing the same label form one region over which the mean of the elements is computed. index : int or sequence of ints, optional Labels of the objects over which the mean is to be computed. Default is None, in which case the mean for all values where label is greater than 0 is calculated.

Returns ------- out : list Sequence of same length as `index`, with the mean of the different regions labeled by the labels in `index`.

See also -------- variance, standard_deviation, minimum, maximum, sum, label

Examples -------- >>> from scipy import ndimage >>> a = np.arange(25).reshape((5,5)) >>> labels = np.zeros_like(a) >>> labels3:5,3:5 = 1 >>> index = np.unique(labels) >>> labels array([0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 1, 1]) >>> index array(0, 1) >>> ndimage.mean(a, labels=labels, index=index) 10.285714285714286, 21.0

val median : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate the median of the values of an array over labeled regions.

Parameters ---------- input : array_like Array_like of values. For each region specified by `labels`, the median value of `input` over the region is computed. labels : array_like, optional An array_like of integers marking different regions over which the median value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the median over the whole array is returned. index : array_like, optional A list of region labels that are taken into account for computing the medians. If index is None, the median over all elements where `labels` is non-zero is returned.

Returns ------- median : float or list of floats List of medians of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a float is returned: the median value of `input` if `labels` is None, and the median value of elements where `labels` is greater than zero if `index` is None.

See also -------- label, minimum, maximum, extrema, sum, mean, variance, standard_deviation

Notes ----- The function returns a Python list and not a NumPy array, use `np.array` to convert the list to an array.

Examples -------- >>> from scipy import ndimage >>> a = np.array([1, 2, 0, 1], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> labels, labels_nb = ndimage.label(a) >>> labels array([1, 1, 0, 2], [1, 1, 0, 2], [0, 0, 0, 2], [3, 3, 0, 0]) >>> ndimage.median(a, labels=labels, index=np.arange(1, labels_nb + 1)) 2.5, 4.0, 6.0 >>> ndimage.median(a) 1.0 >>> ndimage.median(a, labels=labels) 3.0

val median_filter : ?size: [ `Bool of bool | `F of float | `S of string | `Tuple of Py.Object.t | `I of int ] -> ?footprint:[> `Ndarray ] Np.Obj.t -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a multidimensional median filter.

Parameters ---------- input : array_like The input array. size : scalar or tuple, optional See footprint, below. Ignored if footprint is given. footprint : array, optional Either `size` or `footprint` must be defined. `size` gives the shape that is taken from the input array, at every element position, to define the input to the filter function. `footprint` is a boolean array that specifies (implicitly) a shape, but also which of the elements within this shape will get passed to the filter function. Thus ``size=(n,m)`` is equivalent to ``footprint=np.ones((n,m))``. We adjust `size` to the number of dimensions of the input array, so that, if the input array is shape (10,10,10), and `size` is 2, then the actual size used is (2,2,2). When `footprint` is given, `size` is ignored. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- median_filter : ndarray Filtered array. Has the same shape as `input`.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.median_filter(ascent, size=20) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val minimum : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate the minimum of the values of an array over labeled regions.

Parameters ---------- input : array_like Array_like of values. For each region specified by `labels`, the minimal values of `input` over the region is computed. labels : array_like, optional An array_like of integers marking different regions over which the minimum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the minimum over the whole array is returned. index : array_like, optional A list of region labels that are taken into account for computing the minima. If index is None, the minimum over all elements where `labels` is non-zero is returned.

Returns ------- minimum : float or list of floats List of minima of `input` over the regions determined by `labels` and whose index is in `index`. If `index` or `labels` are not specified, a float is returned: the minimal value of `input` if `labels` is None, and the minimal value of elements where `labels` is greater than zero if `index` is None.

See also -------- label, maximum, median, minimum_position, extrema, sum, mean, variance, standard_deviation

Notes ----- The function returns a Python list and not a NumPy array, use `np.array` to convert the list to an array.

Examples -------- >>> from scipy import ndimage >>> a = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> labels, labels_nb = ndimage.label(a) >>> labels array([1, 1, 0, 0], [1, 1, 0, 2], [0, 0, 0, 2], [3, 3, 0, 0]) >>> ndimage.minimum(a, labels=labels, index=np.arange(1, labels_nb + 1)) 1.0, 4.0, 3.0 >>> ndimage.minimum(a) 0.0 >>> ndimage.minimum(a, labels=labels) 1.0

val minimum_filter : ?size: [ `Bool of bool | `F of float | `S of string | `Tuple of Py.Object.t | `I of int ] -> ?footprint:[> `Ndarray ] Np.Obj.t -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a multidimensional minimum filter.

Parameters ---------- input : array_like The input array. size : scalar or tuple, optional See footprint, below. Ignored if footprint is given. footprint : array, optional Either `size` or `footprint` must be defined. `size` gives the shape that is taken from the input array, at every element position, to define the input to the filter function. `footprint` is a boolean array that specifies (implicitly) a shape, but also which of the elements within this shape will get passed to the filter function. Thus ``size=(n,m)`` is equivalent to ``footprint=np.ones((n,m))``. We adjust `size` to the number of dimensions of the input array, so that, if the input array is shape (10,10,10), and `size` is 2, then the actual size used is (2,2,2). When `footprint` is given, `size` is ignored. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- minimum_filter : ndarray Filtered array. Has the same shape as `input`.

Notes ----- A sequence of modes (one per axis) is only supported when the footprint is separable. Otherwise, a single mode string must be provided.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.minimum_filter(ascent, size=20) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val minimum_filter1d : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:int -> input:[> `Ndarray ] Np.Obj.t -> size:int -> unit -> Py.Object.t

Calculate a 1-D minimum filter along the given axis.

The lines of the array along the given axis are filtered with a minimum filter of given size.

Parameters ---------- input : array_like The input array. size : int length along which to calculate 1D minimum axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right.

Notes ----- This function implements the MINLIST algorithm 1_, as described by Richard Harter 2_, and has a guaranteed O(n) performance, `n` being the `input` length, regardless of filter size.

References ---------- .. 1 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.2777 .. 2 http://www.richardhartersworld.com/cri/2001/slidingmin.html

Examples -------- >>> from scipy.ndimage import minimum_filter1d >>> minimum_filter1d(2, 8, 0, 4, 1, 9, 9, 0, size=3) array(2, 0, 0, 0, 1, 1, 0, 0)

val minimum_position : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Find the positions of the minimums of the values of an array at labels.

Parameters ---------- input : array_like Array_like of values. labels : array_like, optional An array of integers marking different regions over which the position of the minimum value of `input` is to be computed. `labels` must have the same shape as `input`. If `labels` is not specified, the location of the first minimum over the whole array is returned.

The `labels` argument only works when `index` is specified. index : array_like, optional A list of region labels that are taken into account for finding the location of the minima. If `index` is None, the ``first`` minimum over all elements where `labels` is non-zero is returned.

The `index` argument only works when `labels` is specified.

Returns ------- output : list of tuples of ints Tuple of ints or list of tuples of ints that specify the location of minima of `input` over the regions determined by `labels` and whose index is in `index`.

If `index` or `labels` are not specified, a tuple of ints is returned specifying the location of the first minimal value of `input`.

See also -------- label, minimum, median, maximum_position, extrema, sum, mean, variance, standard_deviation

Examples -------- >>> a = np.array([10, 20, 30], ... [40, 80, 100], ... [1, 100, 200]) >>> b = np.array([1, 2, 0, 1], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0])

>>> from scipy import ndimage

>>> ndimage.minimum_position(a) (2, 0) >>> ndimage.minimum_position(b) (0, 2)

Features to process can be specified using `labels` and `index`:

>>> label, pos = ndimage.label(a) >>> ndimage.minimum_position(a, label, index=np.arange(1, pos+1)) (2, 0)

>>> label, pos = ndimage.label(b) >>> ndimage.minimum_position(b, label, index=np.arange(1, pos+1)) (0, 0), (0, 3), (3, 1)

val morphological_gradient : ?size:int list -> ?footprint:Py.Object.t -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional morphological gradient.

The morphological gradient is calculated as the difference between a dilation and an erosion of the input with a given structuring element.

Parameters ---------- input : array_like Array over which to compute the morphlogical gradient. size : tuple of ints Shape of a flat and full structuring element used for the mathematical morphology operations. Optional if `footprint` or `structure` is provided. A larger `size` yields a more blurred gradient. footprint : array of ints, optional Positions of non-infinite elements of a flat structuring element used for the morphology operations. Larger footprints give a more blurred morphological gradient. structure : array of ints, optional Structuring element used for the morphology operations. `structure` may be a non-flat structuring element. output : array, optional An array used for storing the output of the morphological gradient may be provided. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the array borders are handled, where `cval` is the value when mode is equal to 'constant'. Default is 'reflect' cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : scalar, optional The `origin` parameter controls the placement of the filter. Default 0

Returns ------- morphological_gradient : ndarray Morphological gradient of `input`.

See also -------- grey_dilation, grey_erosion, gaussian_gradient_magnitude

Notes ----- For a flat structuring element, the morphological gradient computed at a given point corresponds to the maximal difference between elements of the input among the elements covered by the structuring element centered on the point.

References ---------- .. 1 https://en.wikipedia.org/wiki/Mathematical_morphology

Examples -------- >>> from scipy import ndimage >>> a = np.zeros((7,7), dtype=int) >>> a2:5, 2:5 = 1 >>> ndimage.morphological_gradient(a, size=(3,3)) array([0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]) >>> # The morphological gradient is computed as the difference >>> # between a dilation and an erosion >>> ndimage.grey_dilation(a, size=(3,3)) -\ ... ndimage.grey_erosion(a, size=(3,3)) array([0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 0, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]) >>> a = np.zeros((7,7), dtype=int) >>> a2:5, 2:5 = 1 >>> a4,4 = 2; a2,3 = 3 >>> a array([0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 3, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 1, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]) >>> ndimage.morphological_gradient(a, size=(3,3)) array([0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 3, 3, 1, 0], [0, 1, 3, 3, 3, 1, 0], [0, 1, 3, 2, 3, 2, 0], [0, 1, 1, 2, 2, 2, 0], [0, 1, 1, 2, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0])

val morphological_laplace : ?size:[ `I of int | `Is of int list ] -> ?footprint:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Bool of bool ] -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:Py.Object.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional morphological laplace.

Parameters ---------- input : array_like Input. size : int or sequence of ints, optional See `structure`. footprint : bool or ndarray, optional See `structure`. structure : structure, optional Either `size`, `footprint`, or the `structure` must be provided. output : ndarray, optional An output array can optionally be provided. mode : 'reflect','constant','nearest','mirror', 'wrap', optional The mode parameter determines how the array borders are handled. For 'constant' mode, values beyond borders are set to be `cval`. Default is 'reflect'. cval : scalar, optional Value to fill past edges of input if mode is 'constant'. Default is 0.0 origin : origin, optional The origin parameter controls the placement of the filter.

Returns ------- morphological_laplace : ndarray Output

val percentile_filter : ?size: [ `Bool of bool | `F of float | `S of string | `Tuple of Py.Object.t | `I of int ] -> ?footprint:[> `Ndarray ] Np.Obj.t -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> percentile:[ `F of float | `I of int | `Bool of bool | `S of string ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a multidimensional percentile filter.

Parameters ---------- input : array_like The input array. percentile : scalar The percentile parameter may be less then zero, i.e., percentile = -20 equals percentile = 80 size : scalar or tuple, optional See footprint, below. Ignored if footprint is given. footprint : array, optional Either `size` or `footprint` must be defined. `size` gives the shape that is taken from the input array, at every element position, to define the input to the filter function. `footprint` is a boolean array that specifies (implicitly) a shape, but also which of the elements within this shape will get passed to the filter function. Thus ``size=(n,m)`` is equivalent to ``footprint=np.ones((n,m))``. We adjust `size` to the number of dimensions of the input array, so that, if the input array is shape (10,10,10), and `size` is 2, then the actual size used is (2,2,2). When `footprint` is given, `size` is ignored. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- percentile_filter : ndarray Filtered array. Has the same shape as `input`.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.percentile_filter(ascent, percentile=20, size=20) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val prewitt : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate a Prewitt filter.

Parameters ---------- input : array_like The input array. axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.prewitt(ascent) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val rank_filter : ?size: [ `Bool of bool | `F of float | `S of string | `Tuple of Py.Object.t | `I of int ] -> ?footprint:[> `Ndarray ] Np.Obj.t -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> rank:int -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a multidimensional rank filter.

Parameters ---------- input : array_like The input array. rank : int The rank parameter may be less then zero, i.e., rank = -1 indicates the largest element. size : scalar or tuple, optional See footprint, below. Ignored if footprint is given. footprint : array, optional Either `size` or `footprint` must be defined. `size` gives the shape that is taken from the input array, at every element position, to define the input to the filter function. `footprint` is a boolean array that specifies (implicitly) a shape, but also which of the elements within this shape will get passed to the filter function. Thus ``size=(n,m)`` is equivalent to ``footprint=np.ones((n,m))``. We adjust `size` to the number of dimensions of the input array, so that, if the input array is shape (10,10,10), and `size` is 2, then the actual size used is (2,2,2). When `footprint` is given, `size` is ignored. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- rank_filter : ndarray Filtered array. Has the same shape as `input`.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.rank_filter(ascent, rank=42, size=20) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val rotate : ?axes:Py.Object.t -> ?reshape:bool -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?order:int -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?prefilter:bool -> input:[> `Ndarray ] Np.Obj.t -> angle:float -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Rotate an array.

The array is rotated in the plane defined by the two axes given by the `axes` parameter using spline interpolation of the requested order.

Parameters ---------- input : array_like The input array. angle : float The rotation angle in degrees. axes : tuple of 2 ints, optional The two axes that define the plane of rotation. Default is the first two axes. reshape : bool, optional If `reshape` is true, the output shape is adapted so that the input array is contained completely in the output. Default is True. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with `spline_filter` before interpolation. The default is True, which will create a temporary `float64` array of filtered values if `order > 1`. If setting this to False, the output will be slightly blurred if `order > 1`, unless the input is prefiltered, i.e. it is the result of calling `spline_filter` on the original input.

Returns ------- rotate : ndarray The rotated input.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure(figsize=(10, 3)) >>> ax1, ax2, ax3 = fig.subplots(1, 3) >>> img = misc.ascent() >>> img_45 = ndimage.rotate(img, 45, reshape=False) >>> full_img_45 = ndimage.rotate(img, 45, reshape=True) >>> ax1.imshow(img, cmap='gray') >>> ax1.set_axis_off() >>> ax2.imshow(img_45, cmap='gray') >>> ax2.set_axis_off() >>> ax3.imshow(full_img_45, cmap='gray') >>> ax3.set_axis_off() >>> fig.set_tight_layout(True) >>> plt.show() >>> print(img.shape) (512, 512) >>> print(img_45.shape) (512, 512) >>> print(full_img_45.shape) (724, 724)

val shift : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?order:int -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?prefilter:bool -> input:[> `Ndarray ] Np.Obj.t -> shift:[ `F of float | `Sequence of Py.Object.t ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Shift an array.

The array is shifted using spline interpolation of the requested order. Points outside the boundaries of the input are filled according to the given mode.

Parameters ---------- input : array_like The input array. shift : float or sequence The shift along the axes. If a float, `shift` is the same for each axis. If a sequence, `shift` should contain one value for each axis. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with `spline_filter` before interpolation. The default is True, which will create a temporary `float64` array of filtered values if `order > 1`. If setting this to False, the output will be slightly blurred if `order > 1`, unless the input is prefiltered, i.e. it is the result of calling `spline_filter` on the original input.

Returns ------- shift : ndarray The shifted input.

val sobel : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate a Sobel filter.

Parameters ---------- input : array_like The input array. axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.sobel(ascent) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val spline_filter : ?order:Py.Object.t -> ?output:Py.Object.t -> ?mode:Py.Object.t -> input:Py.Object.t -> unit -> Py.Object.t

Multidimensional spline filter.

For more details, see `spline_filter1d`.

See Also -------- spline_filter1d : Calculate a 1-D spline filter along the given axis.

Notes ----- The multidimensional filter is implemented as a sequence of 1-D spline filters. The intermediate arrays are stored in the same data type as the output. Therefore, for output types with a limited precision, the results may be imprecise because intermediate results may be stored with insufficient precision.

Examples -------- We can filter an image using multidimentional splines:

>>> from scipy.ndimage import spline_filter >>> import matplotlib.pyplot as plt >>> orig_img = np.eye(20) # create an image >>> orig_img10, : = 1.0 >>> sp_filter = spline_filter(orig_img, order=3) >>> f, ax = plt.subplots(1, 2, sharex=True) >>> for ind, data in enumerate([orig_img, 'original image'], ... [sp_filter, 'spline filter']): ... axind.imshow(data0, cmap='gray_r') ... axind.set_title(data1) >>> plt.tight_layout() >>> plt.show()

val spline_filter1d : ?order:int -> ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate a 1-D spline filter along the given axis.

The lines of the array along the given axis are filtered by a spline filter. The order of the spline must be >= 2 and <= 5.

Parameters ---------- input : array_like The input array. order : int, optional The order of the spline, default is 3. axis : int, optional The axis along which the spline filter is applied. Default is the last axis. output : ndarray or dtype, optional The array in which to place the output, or the dtype of the returned array. Default is ``numpy.float64``. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge.

Returns ------- spline_filter1d : ndarray The filtered input.

Notes ----- All functions in `ndimage.interpolation` do spline interpolation of the input image. If using B-splines of `order > 1`, the input image values have to be converted to B-spline coefficients first, which is done by applying this 1-D filter sequentially along all axes of the input. All functions that require B-spline coefficients will automatically filter their inputs, a behavior controllable with the `prefilter` keyword argument. For functions that accept a `mode` parameter, the result will only be correct if it matches the `mode` used when filtering.

See Also -------- spline_filter : Multidimensional spline filter.

Examples -------- We can filter an image using 1-D spline along the given axis:

>>> from scipy.ndimage import spline_filter1d >>> import matplotlib.pyplot as plt >>> orig_img = np.eye(20) # create an image >>> orig_img10, : = 1.0 >>> sp_filter_axis_0 = spline_filter1d(orig_img, axis=0) >>> sp_filter_axis_1 = spline_filter1d(orig_img, axis=1) >>> f, ax = plt.subplots(1, 3, sharex=True) >>> for ind, data in enumerate([orig_img, 'original image'], ... [sp_filter_axis_0, 'spline filter (axis=0)'], ... [sp_filter_axis_1, 'spline filter (axis=1)']): ... axind.imshow(data0, cmap='gray_r') ... axind.set_title(data1) >>> plt.tight_layout() >>> plt.show()

val standard_deviation : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[ `I of int | `Is of int list ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate the standard deviation of the values of an N-D image array, optionally at specified sub-regions.

Parameters ---------- input : array_like N-D image data to process. labels : array_like, optional Labels to identify sub-regions in `input`. If not None, must be same shape as `input`. index : int or sequence of ints, optional `labels` to include in output. If None (default), all values where `labels` is non-zero are used.

Returns ------- standard_deviation : float or ndarray Values of standard deviation, for each sub-region if `labels` and `index` are specified.

See Also -------- label, variance, maximum, minimum, extrema

Examples -------- >>> a = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> from scipy import ndimage >>> ndimage.standard_deviation(a) 2.7585095613392387

Features to process can be specified using `labels` and `index`:

>>> lbl, nlbl = ndimage.label(a) >>> ndimage.standard_deviation(a, lbl, index=np.arange(1, nlbl+1)) array( 1.479, 1.5 , 3. )

If no index is given, non-zero `labels` are processed:

>>> ndimage.standard_deviation(a, lbl) 2.4874685927665499

val sum : ?labels:Py.Object.t -> ?index:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Calculate the sum of the values of the array.

Parameters ---------- input : array_like Values of `input` inside the regions defined by `labels` are summed together. labels : array_like of ints, optional Assign labels to the values of the array. Has to have the same shape as `input`. index : array_like, optional A single label number or a sequence of label numbers of the objects to be measured.

Returns ------- sum : ndarray or scalar An array of the sums of values of `input` inside the regions defined by `labels` with the same shape as `index`. If 'index' is None or scalar, a scalar is returned.

See also -------- mean, median

Examples -------- >>> from scipy import ndimage >>> input = 0,1,2,3 >>> labels = 1,1,2,2 >>> ndimage.sum(input, labels, index=1,2) 1.0, 5.0 >>> ndimage.sum(input, labels, index=1) 1 >>> ndimage.sum(input, labels) 6

val uniform_filter : ?size:[ `I of int | `Is of int list ] -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Sequence of Py.Object.t | `S of string ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `I of int | `Sequence of Py.Object.t ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional uniform filter.

Parameters ---------- input : array_like The input array. size : int or sequence of ints, optional The sizes of the uniform filter are given for each axis as a sequence, or as a single number, in which case the size is equal for all axes. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : str or sequence, optional The `mode` parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is 'reflect'. The valid values and their behavior is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int or sequence, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

Returns ------- uniform_filter : ndarray Filtered array. Has the same shape as `input`.

Notes ----- The multidimensional filter is implemented as a sequence of 1-D uniform filters. The intermediate arrays are stored in the same data type as the output. Therefore, for output types with a limited precision, the results may be imprecise because intermediate results may be stored with insufficient precision.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> plt.gray() # show the filtered result in grayscale >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.uniform_filter(ascent, size=20) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

val uniform_filter1d : ?axis:int -> ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:int -> input:[> `Ndarray ] Np.Obj.t -> size:int -> unit -> Py.Object.t

Calculate a 1-D uniform filter along the given axis.

The lines of the array along the given axis are filtered with a uniform filter of given size.

Parameters ---------- input : array_like The input array. size : int length of uniform filter axis : int, optional The axis of `input` along which to calculate. Default is -1. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'reflect'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : int, optional Controls the placement of the filter on the input array's pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right.

Examples -------- >>> from scipy.ndimage import uniform_filter1d >>> uniform_filter1d(2, 8, 0, 4, 1, 9, 9, 0, size=3) array(4, 3, 4, 1, 4, 6, 6, 3)

val variance : ?labels:[> `Ndarray ] Np.Obj.t -> ?index:[ `I of int | `Is of int list ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> Py.Object.t

Calculate the variance of the values of an N-D image array, optionally at specified sub-regions.

Parameters ---------- input : array_like Nd-image data to process. labels : array_like, optional Labels defining sub-regions in `input`. If not None, must be same shape as `input`. index : int or sequence of ints, optional `labels` to include in output. If None (default), all values where `labels` is non-zero are used.

Returns ------- variance : float or ndarray Values of variance, for each sub-region if `labels` and `index` are specified.

See Also -------- label, standard_deviation, maximum, minimum, extrema

Examples -------- >>> a = np.array([1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]) >>> from scipy import ndimage >>> ndimage.variance(a) 7.609375

Features to process can be specified using `labels` and `index`:

>>> lbl, nlbl = ndimage.label(a) >>> ndimage.variance(a, lbl, index=np.arange(1, nlbl+1)) array( 2.1875, 2.25 , 9. )

If no index is given, all non-zero `labels` are processed:

>>> ndimage.variance(a, lbl) 6.1875

val watershed_ift : ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> input:[> `Ndarray ] Np.Obj.t -> markers:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Apply watershed from markers using image foresting transform algorithm.

Parameters ---------- input : array_like Input. markers : array_like Markers are points within each watershed that form the beginning of the process. Negative markers are considered background markers which are processed after the other markers. structure : structure element, optional A structuring element defining the connectivity of the object can be provided. If None, an element is generated with a squared connectivity equal to one. output : ndarray, optional An output array can optionally be provided. The same shape as input.

Returns ------- watershed_ift : ndarray Output. Same shape as `input`.

References ---------- .. 1 A.X. Falcao, J. Stolfi and R. de Alencar Lotufo, 'The image foresting transform: theory, algorithms, and applications', Pattern Analysis and Machine Intelligence, vol. 26, pp. 19-29, 2004.

val white_tophat : ?size:int list -> ?footprint:Py.Object.t -> ?structure:Py.Object.t -> ?output:[> `Ndarray ] Np.Obj.t -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?origin:[ `F of float | `I of int | `Bool of bool | `S of string ] -> input:[> `Ndarray ] Np.Obj.t -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Multidimensional white tophat filter.

Parameters ---------- input : array_like Input. size : tuple of ints Shape of a flat and full structuring element used for the filter. Optional if `footprint` or `structure` is provided. footprint : array of ints, optional Positions of elements of a flat structuring element used for the white tophat filter. structure : array of ints, optional Structuring element used for the filter. `structure` may be a non-flat structuring element. output : array, optional An array used for storing the output of the filter may be provided. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the array borders are handled, where `cval` is the value when mode is equal to 'constant'. Default is 'reflect' cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. origin : scalar, optional The `origin` parameter controls the placement of the filter. Default is 0.

Returns ------- output : ndarray Result of the filter of `input` with `structure`.

See also -------- black_tophat

val zoom : ?output:[ `Ndarray of [> `Ndarray ] Np.Obj.t | `Dtype of Np.Dtype.t ] -> ?order:int -> ?mode:[ `Reflect | `Constant | `Nearest | `Mirror | `Wrap ] -> ?cval:[ `F of float | `I of int | `Bool of bool | `S of string ] -> ?prefilter:bool -> input:[> `Ndarray ] Np.Obj.t -> zoom:[ `F of float | `Sequence of Py.Object.t ] -> unit -> [ `ArrayLike | `Ndarray | `Object ] Np.Obj.t

Zoom an array.

The array is zoomed using spline interpolation of the requested order.

Parameters ---------- input : array_like The input array. zoom : float or sequence The zoom factor along the axes. If a float, `zoom` is the same for each axis. If a sequence, `zoom` should contain one value for each axis. output : array or dtype, optional The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created. order : int, optional The order of the spline interpolation, default is 3. The order has to be in the range 0-5. mode : 'reflect', 'constant', 'nearest', 'mirror', 'wrap', optional The `mode` parameter determines how the input array is extended beyond its boundaries. Default is 'constant'. Behavior for each valid value is as follows:

'reflect' (`d c b a | a b c d | d c b a`) The input is extended by reflecting about the edge of the last pixel.

'constant' (`k k k k | a b c d | k k k k`) The input is extended by filling all values beyond the edge with the same constant value, defined by the `cval` parameter.

'nearest' (`a a a a | a b c d | d d d d`) The input is extended by replicating the last pixel.

'mirror' (`d c b | a b c d | c b a`) The input is extended by reflecting about the center of the last pixel.

'wrap' (`a b c d | a b c d | a b c d`) The input is extended by wrapping around to the opposite edge. cval : scalar, optional Value to fill past edges of input if `mode` is 'constant'. Default is 0.0. prefilter : bool, optional Determines if the input array is prefiltered with `spline_filter` before interpolation. The default is True, which will create a temporary `float64` array of filtered values if `order > 1`. If setting this to False, the output will be slightly blurred if `order > 1`, unless the input is prefiltered, i.e. it is the result of calling `spline_filter` on the original input.

Returns ------- zoom : ndarray The zoomed input.

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt

>>> fig = plt.figure() >>> ax1 = fig.add_subplot(121) # left side >>> ax2 = fig.add_subplot(122) # right side >>> ascent = misc.ascent() >>> result = ndimage.zoom(ascent, 3.0) >>> ax1.imshow(ascent) >>> ax2.imshow(result) >>> plt.show()

>>> print(ascent.shape) (512, 512)

>>> print(result.shape) (1536, 1536)

OCaml

Innovation. Community. Security.

GitHub Discord Twitter Peertube RSS
About
Changelog Releases Industrial Users Academic Users Why OCaml
Ecosystem
Packages Community Events OCaml Planet Jobs
Resources
Install OCaml Get Started Platform Tools Language Manual Standard Library API Books Exercises Papers OCaml Playground Logo
Policies
Carbon Footprint Governance Privacy Code of Conduct