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scipy.ndimage.

# correlate

scipy.ndimage.correlate(input, weights, output=None, mode='reflect', cval=0.0, origin=0, *, axes=None)

  Multidimensional correlation.

  The array is correlated with the given kernel.

  Parameters:
    input array_like

      The input array.

    weights ndarray

      array of weights, same number of dimensions as input

    output array or dtype, optional

      The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created.

    mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional

      The mode parameter determines how the input array is extended beyond its boundaries. Default is ‘reflect’. Behavior for each valid value is as follows:

      ‘reflect’ (d c b a | a b c d | d c b a)

        The input is extended by reflecting about the edge of the last pixel. This mode is also sometimes referred to as half-sample symmetric.

      ‘constant’ (k k k k | a b c d | k k k k)

        The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter.

      ‘nearest’ (a a a a | a b c d | d d d d)

        The input is extended by replicating the last pixel.

      ‘mirror’ (d c b | a b c d | c b a)

        The input is extended by reflecting about the center of the last pixel. This mode is also sometimes referred to as whole-sample symmetric.

      ‘wrap’ (a b c d | a b c d | a b c d)

        The input is extended by wrapping around to the opposite edge.

      For consistency with the interpolation functions, the following mode names can also be used:

      ‘grid-mirror’

        This is a synonym for ‘reflect’.

      ‘grid-constant’

        This is a synonym for ‘constant’.

      ‘grid-wrap’

        This is a synonym for ‘wrap’.

    cval scalar, optional

      Value to fill past edges of input if mode is ‘constant’. Default is 0.0.

    origin int or sequence, optional

      Controls the placement of the filter on the input array’s pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.

    axes tuple of int or None, optional

      If None, input is filtered along all axes. Otherwise, input is filtered along the specified axes. When axes is specified, any tuples used for mode or origin must match the length of axes. The ith entry in any of these tuples corresponds to the ith entry in axes.

  Returns:
    result ndarray

      The result of correlation of input with weights.

  See also

  `convolve`

    Convolve an image with a kernel.

  Notes

  Array API Standard Support

  `correlate` 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.

  Examples

  Correlation is the process of moving a filter mask often referred to as kernel over the image and computing the sum of products at each location.

      >>> from scipy.ndimage import correlate
      >>> import numpy as np
      >>> input_img = np.arange(25).reshape(5,5)
      >>> print(input_img)
      [[ 0  1  2  3  4]
      [ 5  6  7  8  9]
      [10 11 12 13 14]
      [15 16 17 18 19]
      [20 21 22 23 24]]

  Define a kernel (weights) for correlation. In this example, it is for sum of center and up, down, left and right next elements.

      >>> weights = [[0, 1, 0],
      ...            [1, 1, 1],
      ...            [0, 1, 0]]

  We can calculate a correlation result: For example, element `[2,2]` is `7 + 11 + 12 + 13 + 17 = 60`.

      >>> correlate(input_img, weights)
      array([[  6,  10,  15,  20,  24],
          [ 26,  30,  35,  40,  44],
          [ 51,  55,  60,  65,  69],
          [ 76,  80,  85,  90,  94],
          [ 96, 100, 105, 110, 114]])