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
dx 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 higher order derivatives; applied to the
same cross-section of data, the second order derivative, f

x = d
2
f
dx
2
in Figure 4.22(c), is
greatest where the rate of change of the signal is greatest and zero when the rate of change is
constant. The rate of change is constant at the peak of the first order derivative. This is where
there is a zero-crossing