HOUGH TRANSFORM METHODS FOR CURVE DETECTION AND PARAMETER ESTIMATION

Available from UMI in association with The British Library.; In this thesis steps are taken towards a detailed understanding of Hough Transform (HT) methods. A formal definition of the HT is provided along with some useful and interesting results which provide insight into a number of aspects of HT methods. These include the quantisation problem, the use of discrete filters, the nature of efficient coarse-fine implementations and the relationship between the HT and the other detection and estimation methods.; Using this formulation a design methodology based on statistical hypothesis testing is proposed as a means of characterising and optimising HT performance. To illustrate the approach the particular problem of line detection is considered in detail throughout the thesis. This is perhaps the most common and fundamental problem which can be addressed using the HT. The approach is shown to provide formal ways to design optimal HT algorithms. The approach also suggests a fundamental change to the HT which solves the threshold selection problem and yields a method of detection which is independent of object size.; It is also shown that the HT belongs to a larger class of methods which includes some well known techniques from classical statistical estimation. With some generalization HT's can also be considered as robust estimation techniques. This class of techniques have well defined properties. In particular it is shown that the accuracy of parameter estimation can be quantified. This relationship also suggests that iterative methods can be used to improve accuracy without large increases in computation.; A number of alternative implementations which are motivated by the theoretical discussion are tested on real images of manufactured parts. Results demonstrate a clear improvement over existing techniques.; Though line detection is described in the thesis the basic methodology can be used in the study of other problems. In fact its extension to other more complex problems is likely to yield further insights into the nature of HT methods.