The circle detection problem

Abstract

In the previous chapters we discussed the theory of geometric branch-andbound methods and several extensions were given. In this chapter, we now present an application of the suggested techniques. To be more precise, we show how global optimization can be used in image processing to detect imperfect instances of shapes such as lines, circles, or ellipses. We introduce the problem in Section 7.1 and some useful notations are collected in Section 7.2. Before the general problem can be formulated, we have to detect edges in images. To this end, Canny’s edge detection algorithm is briefly summarized in Section 7.3. Next, we can formulate the detection problem as a global optimization problem in Section 7.4. In the following, we also discuss the circle detection problem in detail. Some lower bounds are suggested in Section 7.5 before Section 7.6 illustrates the proposed circle detection problem on several examples.