Multicore DSP

19Hough transform

1. 19.1 Introduction
2. 19.2 Theory
3. 19.3 Limits of r and θ
4. 19.4 Hough transform implementation
5. 19.5 Laboratory experiment
6. 19.6 Conclusion
7. References

19.1 Introduction

In this chapter, the implementation of the Hough transform (HT) is described. However, in order to fully understand the implementation, a review of the algorithm will be given first.

The HT is a popular technique for feature extraction in computer vision and digital image processing. It was first filed for a patent in 1960 by Paul V. C. Hough [1], and used later for the first time by Duda and Hart in 1972 to detect lines and curves in pictures [2]. With the HT, one can detect lines, circles or any structures with a known parametric equation. In this chapter, the implementation is limited to detect lines that will be used for lane detection in automotive applications.

19.2 Theory

Consider the Cartesian representation in Figure 19.1. P_i represents a point with the coordinates (x_i,y_i). There are an infinite number of lines passing by the point P_i. Each line can be fully represented by r (the normal to a line passing the point P_i) and the angle θ, as shown in Figure 19.1.

Figure 19.1 Cartesian representation of a line.

Let’s express a line passing by the point P_i in terms of r and θ (see Equations (19.1), (19.2) and (19.3)) and then generalise this for each line.

(19.1)

Also:

(19.2) ...