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# scipy.ndimage.morphology.grey_dilation

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

  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 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. output : array, optional An array used for storing the ouput 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
  Returns : | output : ndarray Grayscale dilation of input.

  See also

  `binary_dilation`, `grey_erosion`, `grey_closing`, `grey_opening`, `generate_binary_structure`, `ndimage.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 [R49] is a mathematical morphology operation [R50].

  References

  [R49] | (1, 2) http://en.wikipedia.org/wiki/Dilation_%28morphology%29

  [R50] | (1, 2) http://en.wikipedia.org/wiki/Mathematical_morphology

  Examples

      >>> 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.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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