package scipy

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Multi-dimensional 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])

Multi-dimensional 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.])

Multi-dimensional 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])

Fill the holes in binary objects.

Parameters ---------- input : array_like n-dimensional 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])

Multi-dimensional 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])

Multi-dimensional 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])

Multi-dimensional 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])

Multi-dimensional 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

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.

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`.

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]])

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)

Multi-dimensional greyscale closing.

A greyscale closing consists in the succession of a greyscale dilation, and a greyscale 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

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])

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])

Multi-dimensional greyscale opening.

A greyscale opening consists in the succession of a greyscale erosion, and a greyscale 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

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])

Multi-dimensional 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])

Multi-dimensional 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

Multi-dimensional 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