Motion analysis and stereopsis without matching: implications for models of vision

The analysis of visual motion and stereopsis are two of the most important problems the visual system has to solve. They share the goal of inferring some aspect of the structure of the world from the relations between two or more images. The approach taken by Marr (1982) is based on a particular model of visual inference in which motion (or depth) is inferred from the relative displacement between identical features in the two images. An alternative formalism for solving problems of low level vision has been proposed by the authors based not on Boolean lattices of propositions, but on non-distributive lattices associated with the subspaces of the vector space of images. This leads to visual representations based on what may loosely be described as `local Fourier spectra´. These representations can be shown to minimise the uncertainties (ambiguities) associated with visual inference; they are robust in noise; they lead to a distributed symbolic representation of the kind currently being discussed in `neural nets´ models of perception. Moreover, effective algorithms for feature description, texture analysis and motion analysis have been proposed using such methods. Finally, it has been argued that they also provide a more plausible account of the properties of biological vision systems. A brief review is presented of the principal ideas of the new theory