scipy.ndimage.morphology.morphological_gradient

scipy.ndimage.morphology.morphological_gradient(input, size=None, footprint=None, structure=None, output=None, mode='reflect', cval=0.0, origin=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 ouput 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, ndimage.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

[R85]

http://en.wikipedia.org/wiki/Mathematical_morphology

Examples

>>> a = np.zeros((7,7), dtype=np.int)
>>> a[2:5, 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=np.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.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]])