Towards a new framework of the Hough transform

This paper´s main contributions are three-fold. Firstly, it is shown that the two existing template matching-like definitions of the Hough transform proposed by Princen, Illingworth and Kittler (1992) and by Bergen and Shvaytser (1991) are inadequate. The principal reason behind this is that the common implicit assumption of these two definitions, that every feature point within the template associated with a given accumulator cell E₀ in Hough space votes equally to E₀, is not reasonable. Secondly, an inherent probabilistic aspect of the Hough transform embedded in the transformation process from the image space to the parameter space is clarified. It is concluded that when the Hough transform is used to detect a pattern, an appropriate curve (surface, if the number of the parameters to be detected is more than 2) density function, which depends on the parameterization of the pattern, must be implicitly or explicitly provided to eliminate the uncertainties resulting from such a probabilistic aspect. Thirdly, a new framework of the Hough transform is proposed which mainly consists of two parts, namely parameterization and associated curve (surface) density function