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# scipy.ndimage.morphology.grey_erosion

`scipy.ndimage.morphology.``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 : | input : array_like Array over which the grayscale erosion is to be computed. size : tuple of ints Shape of a flat and full structuring element used for the grayscale erosion. Optional if footprint is provided. footprint : array 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. structure : array of ints, optional Structuring element used for the grayscale erosion. structure may be a non-flat structuring element. output : array, optional An array used for storing the ouput 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’ 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 Grayscale erosion of input.

  See also

  `binary_erosion`, `grey_dilation`, `grey_opening`, `grey_closing`, `generate_binary_structure`, `ndimage.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 [R51] is a mathematical morphology operation [R52].

  References

  [R51] | (1, 2) http://en.wikipedia.org/wiki/Erosion_%28morphology%29

  [R52] | (1, 2) http://en.wikipedia.org/wiki/Mathematical_morphology

  Examples

      >>> a = np.zeros((7,7), dtype=np.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]])

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