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scipy.ndimage.

# convolve

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

  Multidimensional convolution.

  The array is convolved with the given kernel.

  Parameters:
    input array_like

      The input array.

    weights array_like

      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 right, and negative ones to the left. 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 convolution of input with weights.

  See also

  `correlate`

    Correlate an image with a kernel.

  Notes

  Each value in result is \(C_i = \sum_j{I_{i+k-j} W_j}\), where W is the weights kernel, j is the N-D spatial index over \(W\), I is the input and k is the coordinate of the center of W, specified by origin in the input parameters.

  Examples

  Perhaps the simplest case to understand is `mode='constant', cval=0.0`, because in this case borders (i.e., where the weights kernel, centered on any one value, extends beyond an edge of input) are treated as zeros.

      >>> import numpy as np
      >>> a = np.array([[1, 2, 0, 0],
      ...               [5, 3, 0, 4],
      ...               [0, 0, 0, 7],
      ...               [9, 3, 0, 0]])
      >>> k = np.array([[1,1,1],[1,1,0],[1,0,0]])
      >>> from scipy import ndimage
      >>> ndimage.convolve(a, k, mode='constant', cval=0.0)
      array([[11, 10,  7,  4],
             [10,  3, 11, 11],
             [15, 12, 14,  7],
             [12,  3,  7,  0]])

  Setting `cval=1.0` is equivalent to padding the outer edge of input with 1.0’s (and then extracting only the original region of the result).

      >>> ndimage.convolve(a, k, mode='constant', cval=1.0)
      array([[13, 11,  8,  7],
             [11,  3, 11, 14],
             [16, 12, 14, 10],
             [15,  6, 10,  5]])

  With `mode='reflect'` (the default), outer values are reflected at the edge of input to fill in missing values.

      >>> b = np.array([[2, 0, 0],
      ...               [1, 0, 0],
      ...               [0, 0, 0]])
      >>> k = np.array([[0,1,0], [0,1,0], [0,1,0]])
      >>> ndimage.convolve(b, k, mode='reflect')
      array([[5, 0, 0],
             [3, 0, 0],
             [1, 0, 0]])

  This includes diagonally at the corners.

      >>> k = np.array([[1,0,0],[0,1,0],[0,0,1]])
      >>> ndimage.convolve(b, k)
      array([[4, 2, 0],
             [3, 2, 0],
             [1, 1, 0]])

  With `mode='nearest'`, the single nearest value in to an edge in input is repeated as many times as needed to match the overlapping weights.

      >>> c = np.array([[2, 0, 1],
      ...               [1, 0, 0],
      ...               [0, 0, 0]])
      >>> k = np.array([[0, 1, 0],
      ...               [0, 1, 0],
      ...               [0, 1, 0],
      ...               [0, 1, 0],
      ...               [0, 1, 0]])
      >>> ndimage.convolve(c, k, mode='nearest')
      array([[7, 0, 3],
             [5, 0, 2],
             [3, 0, 1]])