# scipy.ndimage.convolve

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

  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, optional

      Controls the origin of the input signal, which is where the filter is centered to produce the first element of the output. Positive values shift the filter to the right, and negative values shift the filter to the left. Default is 0.

  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]])