Bayesian and non-Bayesian probabilistic models for medical 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 some quantitative tasks. In this paper we demonstrate examples of Bayesian and non-Bayesian techniques from the area of magnetic resonance image (MRI) analysis. Issues raised by these examples are used to illustrate 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. q 2003 Elsevier B.V. All rights reserved.