scipy.ndimage.grey_erosion

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

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(1,2)

https://en.wikipedia.org/wiki/Erosion_%28morphology%29

2(1,2)

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]])