Randomized Hough Transform (RHT): Basic Mechanisms, Algorithms, and Computational Complexities

Abstract

Recently, a new curve detection approach called the randomized Hough transform (RHT) was heuristically proposed by the authors, inspired by the efforts of using neural computation learning techniques for curve detection. The preliminary experimental results and some qualitative analysis showed that in comparison with the Hough transform (HT) and its variants, the RHT has advantages of fast speed, small storage, infinite range of the parameter space, and high parameter resolution, and it can overcome several difficulties encountered with the HT methods. In this paper, the basic ideas of RHT are further developed into a more systematic and theoretically supported new method for curve detection. The fundamental framework and the main components of this method are elaborated. The advantages of RHT are further confirmed. The basic mechanisms behind these advantages are exposed by both theoretical analysis and detailed experimental demonstrations. The main differences between RHT and some related techniques are elucidated. This paper also proposes several improved algorithms for implementing RHT for curve detection problems in noisy images. They are tested by experiments on images with various kinds of strong noise. The results show that the advantages of RHT are quite robust. Moreover, the implementations of these algorithms are modeled by a generalized Bernoulli process, allowing probability analysis on these algorithms to estimate their computational complexities and to decide some important parameters for their implementations. It is shown quantitatively that the complexities are considerably smaller than those of the HT.