A Unified Mathematical Approach to Image Analysis.

Abstract : This report describes a unified approach to the mathematical modelling and statistical analysis of pictures. The results reported here were derived from the research project 'Nonparametric Estimation by the Model of Sieves' supported by the U.S. Army Research Office, Contract DAAG29-83K-0116 to Brown University. Early in the project, the investigations focused on the estimation of (properties of) digitized images; this focus was a natural extension of our earlier work on the method of sieves of regularizing statistical estimates of infinite dimensional objects and the groundwork that had been laid for General Pattern Theory. The present report presents the Bayesian paradigm for mathematical modeling and analysis of digital images and then describes four instances of the paradigm in detail. Directions for ongoing and future research are also indicated. Keywords: Image processing; Algorithms; Segmentation; Boundary detection; tomography; Global image analysis.