1D and pseudo-2D hidden Markov models for image analysis : Theoretical introduction

This document presents a comprehensive approach to Hidden Markov Modelling. Concepts are first introduced in a one-dimensional context. Both model evaluation and training are considered and theoretical developments which lead to algorithms are presented. Major implementation issues are also addressed. Then, results are extended to two-dimensional Hidden Markov Modelling. Again, model evaluation and training are considered and corresponding algorithms sketched. Proofs and detailed justifications of results presented can be found in the referenced bibliography. This report is the first part of a three-fold document. Part Two [8] details the implementation of the tools presented in this document and part Three [9] specialises in applying these procedures to colour image analysis.