# (a) Principle of the Hough transform

Hough transform was proposed by P.V.C. Hough in 1962 [11] for image characteristic detection. It is widely used in digital image processing, especially in dealing

**Fig. 3.12 ****Hough Transform**

with straight line indication and parameter estimation. The principle of Hough transform is shown in Fig. 3.12.

In Fig. 3.12, F(x, y) is a function of straight line on Plane (x, y). O is the origin of Plane (x, y). p is the length of the normal of F(x, y) to point O, and *в* is the angle between normal and axis y. Hough transform is a transform from Plane (x, y) to Plane (*p*, *в*). It is supposed that

By using Eq. 3.5.1, each point in Plane (x, y) corresponds to a sinusoid in Plane (p, в). Therefore, all points in Plane (x,y) correspond to a series of sinusoid interweaved together in Plane (p, в). If points in Plane (x, y) follows the straight line function F(x, y), it appears a peak in Plane (p, в). By indicating the coordinates of the peak, the parameters of F(x, y) can be estimated.

After range compression and range cell curve correction, the echo of moving target is a slant line, and its slope represents linear RCM. By using the Hough transform, the cross-track velocity can be estimated.