Introduction

A task of visual perception is to find the scene which best explains visual observations. Figure 9.1 can be used to illustrate the problem of perception. The visual data is the image held by two cherubs at the right. Scattered in the middle are various geometrical objects – “scene interpretations” – which may account for the observed data. How does one choose between the competing interpretations for the image data?

One approach is to find the probability that each interpretation could have created the observed data. Bayesian statistics are a powerful tool for this, e.g. Geman & Geman (1984), Jepson & Richards (1992), Kersten (1991), Szeliski (1989). One expresses prior assumptions as probabilities and calculates for each interpretation a posterior probability, conditioned on the visual data. The best interpretation may be that with the highest probability density, or a more sophisticated criterion may be used. Other computational techniques, such as regularization (Poggio et al., 1985; Tikhonov & Arsenin, 1977), can be posed in a Bayesian framework (Szeliski, 1989). In this chapter, we will apply the powerful assumption of “generic view” in a Bayesian framework. This will lead us to an additional term from Bayesian theory involving the Fisher information matrix. (See also chapter 7 by Blake et al..) This will modify the posterior probabilities to give additional information about the scene.