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scipy.ndimage.

# grey_dilation

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

  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].

  Array API Standard Support

  `grey_dilation` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ⛔
  JAX | ⚠️ no JIT | ⛔
  Dask | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  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]])