The Hough Transform and Its Nature

Abstract

This chapter discusses the nature of the Hough transform (HT). It develops the generalized Hough transform (GHT), which can be used to find all shapes, and shows how it is related to the spatial matched filter, hence leading to optimal detection sensitivity. This means that gradient rather than uniform weighting should be used in parameter space. As an example, the chapter describes the application of the GHT to ellipse detection. It then compares the computational loads of three ellipse detection methods: while the computational load of the GHT will generally be much lower than that of the diameter bisection method, and far lower than that of the chord–tangent method, other factors such as discriminability are involved. The diameter bisection method has lower discriminability—an advantage if superellipses are to be detected. The chapter also considers the value of the Gerig and Klein back-projection technique in cutting down the effects of clutter.