Image Processing Reference
In-Depth Information
(a) Hysteresis thresholding,
upper level = 40, lower level = 10
(b) Uniform thresholding,
level = 40
(c) Uniform thresholding,
level = 10
Figure 4.20
Comparing hysteresis thresholding with uniform thresholding
3 × 3 Sobel operator with uniform thresholding. The retention of major detail by the Canny
operator is very clear; the face is virtually recognisable in Figure 4.21 (b) whereas it is less
clear in Figure 4.21 (c).
(a) Original image
(b) Canny
(c) Sobel
Figure 4.21
Comparing Canny with Sobel
4.3
Second-order edge detection operators
4.3.1
Motivation
First-order edge detection is based on the premise that differentiation highlights change;
image intensity changes in the region of a feature boundary. The process is illustrated in
Figure 4.22 where Figure 4.22 (a) is a cross-section through image data. The result of first-
order edge detection, f ′ ( x ) = d f /d x in Figure 4.22 (b), is a peak where the rate of change of
the original signal, f ( x ) in Figure 4.22 (a), is greatest. There are of course higher order
derivatives; applied to the same cross-section of data, the second-order derivative, f ″( x ) =
 
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