The morphological Beucher gradient can be computed as a difference image of the dilated version and the eroded version of an input grayscale image. SciPy ndimage provides a function for computing the morphological gradient of a grayscale image. The following code block shows how these two produce the same output for an Einstein image:

from scipy import ndimage
im = rgb2gray(imread('../images/einstein.jpg'))
im_d = ndimage.grey_dilation(im, size=(3,3))
im_e = ndimage.grey_erosion(im, size=(3,3))
im_bg = im_d - im_e
im_g = ndimage.morphological_gradient(im, size=(3,3))
pylab.gray()
pylab.figure(figsize=(20,18))
pylab.subplot(231), pylab.imshow(im), pylab.title('original', size=20),
pylab.axis('off')
pylab.subplot(232), pylab.imshow(im_d), pylab.title('dilation', size=20),
pylab.axis('off')
pylab.subplot(233), pylab.imshow(im_e), pylab.title('erosion', size=20),
pylab.axis('off')
pylab.subplot(234), pylab.imshow(im_bg), pylab.title('Beucher gradient (bg)', size=20), pylab.axis('off')
pylab.subplot(235), pylab.imshow(im_g), pylab.title('ndimage gradient (g)', size=20), pylab.axis('off')
pylab.subplot(236), pylab.title('diff gradients (bg - g)', size=20), pylab.imshow(im_bg - im_g) 
pylab.axis('off')
pylab.show()

The following screenshot shows the output—the SciPy morphological gradient function has the exact same output image as the Beucher gradient: