scipy.signal.convolve2d(in1, in2, mode='full', boundary='fill', fillvalue=0)[source]

Convolve two 2-dimensional arrays.

Convolve in1 and in2 with output size determined by mode, and boundary conditions determined by boundary and fillvalue.


in1, in2 : array_like

Two-dimensional input arrays to be convolved.

mode : str {‘full’, ‘valid’, ‘same’}, optional

A string indicating the size of the output:


The output is the full discrete linear convolution of the inputs. (Default)


The output consists only of those elements that do not rely on the zero-padding.


The output is the same size as in1, centered with respect to the ‘full’ output.

boundary : str {‘fill’, ‘wrap’, ‘symm’}, optional

A flag indicating how to handle boundaries:


pad input arrays with fillvalue. (default)


circular boundary conditions.


symmetrical boundary conditions.

fillvalue : scalar, optional

Value to fill pad input arrays with. Default is 0.


out : ndarray

A 2-dimensional array containing a subset of the discrete linear convolution of in1 with in2.


Compute the gradient of an image by 2D convolution with a complex Scharr operator. (Horizontal operator is real, vertical is imaginary.) Use symmetric boundary condition to avoid creating edges at the image boundaries.

>>> from scipy import signal
>>> from scipy import misc
>>> face = misc.face(gray=True)
>>> scharr = np.array([[ -3-3j, 0-10j,  +3 -3j],
...                    [-10+0j, 0+ 0j, +10 +0j],
...                    [ -3+3j, 0+10j,  +3 +3j]]) # Gx + j*Gy
>>> grad = signal.convolve2d(face, scharr, boundary='symm', mode='same')
>>> import matplotlib.pyplot as plt
>>> fig, (ax_orig, ax_mag, ax_ang) = plt.subplots(1, 3)
>>> ax_orig.imshow(face, cmap='gray')
>>> ax_orig.set_title('Original')
>>> ax_orig.set_axis_off()
>>> ax_mag.imshow(np.absolute(grad), cmap='gray')
>>> ax_mag.set_title('Gradient magnitude')
>>> ax_mag.set_axis_off()
>>> ax_ang.imshow(np.angle(grad), cmap='hsv') # hsv is cyclic, like angles
>>> ax_ang.set_title('Gradient orientation')
>>> ax_ang.set_axis_off()

(Source code)