An inherent probabilistic aspect of the Hough transform

in this paper a new property of the Hough transform is discovered, namely an inherent probabilistic aspect which is independent of the input image and embedded in the transformation process from the image space to the parameter space. It is shown that such a probabilistic aspect has a wide range of implica tions concerning the specification of implementation schemes and the performance of Hough transform. In particular, it is shown that in order to make the Hough transform really meaningful, an appropriate curve (surface) density function must be, either explicitly or implicitly, supplied during its implementation processi and that the widely used approach to uniformly discretizing parameter space in the literature is generally inadequate.