Probabilistic approach to the Hough transform

Abstract

It is shown that there is a strong relationship between the Hough transform and the maximum likelihood method. The Probabilistic Hough Transform (PHT), a mathematically ‘correct’ form of the Hough transform, is defined as a likelihood function in the output parameters. A model of feature error characteristics is proposed, combining normally distributed measurement errors with uniformly distributed correspondence errors. A PHT is illustrated in the familiar problem of finding straight lines from oriented edgels, and it is shown that the conventional Hough method gives a good approximation to the PHT. In situations where there are many unknown parameters, however, conventional methods do not perform well. The PHT has been successfully applied to a tracking problem involving a six dimensional Hough space, and shows a considerable improvement in robustness over a conventional method.