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Module « scipy.ndimage »

Fonction grey_dilation - module scipy.ndimage

Signature de la fonction grey_dilation

def grey_dilation(input, size=None, footprint=None, structure=None, output=None, mode='reflect', cval=0.0, origin=0, *, axes=None) 

Description

help(scipy.ndimage.grey_dilation)

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. The `structure` array applies an
    additive offset for each pixel in the neighborhood.
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
axes : tuple of int or None
    The axes over which to apply the filter. If None, `input` is filtered
    along all axes. If an `origin` tuple is provided, its length must match
    the number of axes.

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 {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 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
>>> import numpy as np
>>> a = np.zeros((7,7), dtype=int)
>>> a[2:5, 2:5] = 1
>>> a[4,4] = 2; a[2,3] = 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]])

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