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# 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 : | output : 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

  [R71] | 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]])

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