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 inf erence of scene properties from retinal images is not deductive; it require s knowledge about the external environment. Further, it has been suggested that the environment must be regular in some way in order for any scene pro perties to be reliably inferred. In particular, Knill and Kersten [1991, in Pattern Recognition by Man and Machine Ed. R J Watt (London: Macmillan)] a nd Jepson et al [1996, in Bayesian Approaches to Perception Eds D Knill, W Richards (Cambridge: Cambridge University Press)] claim that, given an 'unb iased' prior probability distribution for the scenes being observed, the ge neric viewpoint assumption is not probabilistically valid. However, this cl aim depends upon the use of representation spaces that may not be appropria te for the problems they consider. In fact, it is problematic to define a r igorous criterion for a probability distribution to be considered'random' o r 'regularity-free' in many natural domains of interest. This problem is cl osely related to Bertrand's paradox. I propose that, in the case of 'unbias ed' priors, the reliability of inferences based on the generic viewpoint as sumption depends partly on whether or not an observed coincidence in the im age involves features known to be on the same object. This proposal is base d 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 considerati ons arise in the case of inferring 3-D motion from image motion.