scipy.ndimage.convolve¶

scipy.ndimage.
convolve
(input, weights, output=None, mode='reflect', cval=0.0, origin=0)[source]¶ Multidimensional convolution.
The array is convolved with the given kernel.
 Parameters
 inputarray_like
The input array.
 weightsarray_like
Array of weights, same number of dimensions as input
 outputarray 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.
 modestr or sequence, optional
The mode parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is ‘reflect’. The valid values and their behavior 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.
 ‘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.
 ‘wrap’ (a b c d  a b c d  a b c d)
The input is extended by wrapping around to the opposite edge.
 cvalscalar, optional
Value to fill past edges of input if mode is ‘constant’. Default is 0.0
 originint 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.
 Returns
 resultndarray
The result of convolution of input with weights.
See also
correlate
Correlate an image with a kernel.
Notes
Each value in result is \(C_i = \sum_j{I_{i+kj} W_j}\), where W is the weights kernel, j is the nD 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.>>> 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]])