Hypothesis testing: a framework for analysing and optimising Hough transform performance

A formal, quantitative approach to designing optimal Hough transform (HT) algorithms is proposed. This approach takes the view that a HT is a hypothesis testing method. This view allows the performance of HT algorithms to be quantified. The power function, which gives the probability of rejection as a function of the underlying parametric distribution of data points, is shown to be the fundamentally important characteristic of HT behavior. Attempting to make the power function narrow is a formal approach to optimizing HT performance. To illustrate how this framework is useful the particular problem of line detection is discussed. It is shown that the hypothesis testing framework leads to a redefinition of HT in which the values are a measure of the distribution of points around a curve rather than the number of points on a curve. The solution to many HT design problems can be posed within the framework, including optimal quantizations and optimum sampling of the parameter space. Consideration is given to the design of optimum 1-D filters which can be used to sharpen the peak structure in parameter space. Results on several real images illustrate the improvements obtained