Markovian Models for Image Analysis

Objectives

Master the main concepts and tools of Markov/Gibbsian modeling, limited to the case of finite dependency graphs.

Know how to use them on various archetypal problems (texture modeling and classification, grayscale segmentation, image restoration with discontinuity preservation, etc.).

Practical case studies

Course outline

At the frontiers of statistical physics, probability theory and signal processing, Markov fields and Gibbs distributions provide a probabilistic framework well suited to describing and solving image analysis problems where a considerable number of variables, observed or unobserved, interact locally. The resulting Markov properties make it possible to define techniques for sampling, Bayesian estimation of unobserved variables, and estimation of the parameters involved. This course covers the following topics: Gaussian Markov fields on grids, Markov fields on graphs, inverse problems and Bayesian estimation.

Prerequisites

Markov chains, multivariate exploratory statistics