Low-level feature extraction (including edge detection) - Feature Extraction and Image Processing - page 110

Sobel(pic,winsize):=

w2 floor winsize
2

edge_mag ← zero(pic)
edge_dir ← zero(pic)
for x ∈ w2..cols(pic)-1-w2
for y ∈ w2..rows(pic)-1-w2
x_mag ← Sobel_x(submatrix(pic,y-w2,y+w2,x-w2,x+w2))

y_mag ←

Sobel_y(submatrix(pic,y-w2,y+w2,x-w2,x+w2))

magnitude(x_mag, y_mag)
mag_normalise

edge_mag y_x ← floor

edge_dir y,x ←

direction(x_mag,y_mag)

(edge_mag edge_dir)

Code 4.8 Generalised Sobel operator

shown in the edge magnitude image, Figure 4.11 (b). When this is thresholded at a suitable
value, many edge points are found, as shown in Figure 4.11 (c). Note that in areas of the
image where the brightness remains fairly constant, such as the cheek and shoulder, there
is little change which is reflected by low edge magnitude and few points in the thresholded
data.

(a) Original image (b) Sobel edge magnitude (c) Thresholded magnitude

Figure 4.11 Applying the Sobel operator

The Sobel edge direction data can be arranged to point in different ways, as can the
direction provided by the Prewitt operator. If the templates are inverted to be of the form
shown in Figure 4.12 , the edge direction will be inverted around both axes. If only one of
the templates is inverted, then the measured edge direction will be inverted about the
chosen axis.
This gives four possible directions for measurement of the edge direction provided by
the Sobel operator, two of which (for the templates of Figures 4.10 and 4.12 ) are illustrated