The generic viewpoint assumption and Bayesian inference

The task of human vision is to reliably infer useful information about the external environment from images formed on the retinae. In general, the inference of scene properties from retinal images is not deductive; it requires knowledge about the external environment. Further, it has been suggested that the environment must be regular in some way in order for any scene properties to be reliably inferred. In particular, Knill and Kersten [1991, in Pattern Recognition by Man and Machine Ed. R J Watt (London: Macmillan)] and Jepson et al [1996, in Bayesian Approaches to Perception Eds D Knill, W Richards (Cambridge: Cambridge University Press)] claim that, given an 'unbiased' prior probability distribution for the scenes being observed, the generic viewpoint assumption is not probabilistically valid. However, this claim depends upon the use of representation spaces that may not be appropriate for the problems they consider. In fact, it is problematic to define a rigorous criterion for a probability distribution to be considered 'random' or 'regularity-free' in many natural domains of interest. This problem is closely related to Bertrand's paradox. I propose that, in the case of 'unbiased' priors, the reliability of inferences based on the generic viewpoint assumption depends partly on whether or not an observed coincidence in the image involves features known to be on the same object. This proposal is based on important differences between the distributions associated with: (i) a 'random' placement of features in 3-D, and (ii) the positions of features on a 'randomly shaped' and 'randomly posed' 3-D object. Similar considerations arise in the case of inferring 3-D motion from image motion.