Probabilistic relaxation and the Hough transform

Abstract

We discuss the recent developments in probabilistic relaxation which is used as a tool for contextual sensory data interpretation. The relationship of this technique with the Hough transform is then established, focusing on the Generalised Hough Transform (GHT). We show that the label probability updating formula of the probabilistic relaxation process exploiting binary relations between object primitives, under the assumption that the primitives convey weak context, exhibits very close similarity to the voting function employed by a computationally efficient GHT. We argue that the relationship could be exploited by importing the positive features of the respective techniques to benefit one another. Specific suggestions for enhancing the respective techniques are mentioned. They include the adoption of the representational efficiency of the Hough transform to reduce the computational complexity of probabilistic relaxation. Vice versa, in the case of the Generalised Hough transform it is pointed out that the effect of an unknown object transformation could be dealt with by means of a parallel cooperative interpretation rather than by means of an exhaustive search through the parameter space of a transformation group. This has implications in terms of both the storage and computational requirements of the GHT. It also opens the possibility of using the GHT for detecting objects subject to more complex transformations such as affine or perspective. The relationship also suggests the possibility of using alternative voting functions which may speed up the object detection process.