Skip to main content
`Ctrl`+`K`
scipy.ndimage.

# morphological_gradient

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

  Multidimensional 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. The structure array applies offsets to the pixels in a neighborhood (the offset is additive during dilation and subtractive during erosion)

    output array, optional

      An array used for storing the output 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

    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:
    morphological_gradient ndarray

      Morphological gradient of input.

  See also

  `grey_dilation`, `grey_erosion`, `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.

  Array API Standard Support

  `morphological_gradient` 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/Mathematical_morphology

  Examples

      >>> from scipy import ndimage
      >>> import numpy as np
      >>> a = np.zeros((7,7), dtype=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=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]])