Added a second example to the edge filtering gallery example, focusing on

the difference between Scharr and Sobel filters.

doc/examples/plot_edge_filter.py

@@ -8,10 +8,11 @@ They are discrete differentiation operators, computing an approximation of the
 gradient of the image intensity function.
 
 """
+import numpy as np
 import matplotlib.pyplot as plt
 
 from skimage.data import camera
-from skimage.filters import roberts, sobel
+from skimage.filters import roberts, sobel, scharr
 
 
 image = camera()
@@ -28,4 +29,49 @@ ax1.imshow(edge_sobel, cmap=plt.cm.gray)
 ax1.set_title('Sobel Edge Detection')
 ax1.axis('off')
 
+plt.tight_layout()
+
+"""
+.. image:: PLOT2RST.current_figure
+
+Different operators compute different finite-difference approximations of the
+gradient. For example, the Scharr filter results in a better rotational
+variance than other filters such as the Sobel filter. The difference between
+the two filters is illustrated below on an image that is the discretization of
+a rotation-invariant continuous function. The discrepancy between the two
+filters is stronger for regions of the image where the direction of the
+gradient is close to diagonals, and for regions with high spatial frequencies.
+"""
+
+x, y = np.ogrid[:100, :100]
+# Rotation-invariant image with different spatial frequencies
+img = np.exp(1j * np.hypot(x, y)**1.3 / 20.).real
+
+edge_sobel = sobel(img)
+edge_scharr = scharr(img)
+
+fig, ((ax0, ax1), (ax2, ax3)) = plt.subplots(nrows=2, ncols=2)
+
+ax0.imshow(edge_sobel, cmap=plt.cm.gray)
+ax0.set_title('Sobel Edge Detection')
+ax0.axis('off')
+
+ax1.imshow(edge_scharr, cmap=plt.cm.gray)
+ax1.set_title('Scharr Edge Detection')
+ax1.axis('off')
+
+ax2.imshow(img, cmap=plt.cm.gray)
+ax2.set_title('Original image')
+ax2.axis('off')
+
+ax3.imshow(edge_scharr - edge_sobel, cmap=plt.cm.jet)
+ax3.set_title('difference (Scharr - Sobel)')
+ax3.axis('off')
+
+plt.tight_layout()
+
 plt.show()
+
+"""
+.. image:: PLOT2RST.current_figure
+"""