scipy.ndimage.grey_erosion#

scipy.ndimage.grey_erosion(input, size=None, footprint=None, structure=None, output=None, mode='reflect', cval=0.0, origin=0)[source]#

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

inputarray_like: Array over which the grayscale erosion is to be computed.
sizetuple of ints: Shape of a flat and full structuring element used for the grayscale erosion. Optional if footprint or structure is provided.
footprintarray 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.
structurearray of ints, optional: Structuring element used for the grayscale erosion. structure may be a non-flat structuring element.
outputarray, 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’
cvalscalar, optional: Value to fill past edges of input if mode is ‘constant’. Default is 0.0.
originscalar, optional: The origin parameter controls the placement of the filter. Default 0

Returns

outputndarray: 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 {input(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)
>>> a[1:6, 1:6] = 3
>>> a[4,4] = 2; a[2,3] = 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]])

scipy.ndimage.grey_dilation

scipy.ndimage.grey_opening