Bayesian and Non-Bayesian Probabilistic Models for Image Analysis

Bayesian approaches to data analysis are popular in machine vision, and yet the main advantage of Bayes theory, the ability to incorporate prior knowledge in the form of the prior probabilities, may lead to problems in quantitative tasks. In this paper we demonstrate examples of Bayesian and nonBayesian techniques with the use of selected examples from the area of magnetic resonance image (MRI) analysis. Issues raised by these examples are used to illustrate common difficulties in Bayesian methods and to motivate an approach based on frequentist methods. We believe this approach to be more suited to quantitative data analysis, and provide a general theory for the use of these methods in learning (Bayes risk) systems and for data fusion. Proofs are given for the more novel aspects of the theory. We conclude with a discussion of the strengths and weaknesses, and the fundamental suitability, of Bayesian and non-Bayesian approaches for MRI analysis in particular, and for machine vision systems in general. Overall we advise caution regarding the common assertion that the best approaches to all machine vision problems are necessarily Bayesian.