(Created 2008-07-17.)
 STATISTICAL IMAGE ANALYSIS FMS150

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course might be given in English. FMS150 overlap following cours/es: MAS228, MAS228 och MASM13. Optional for: C4, D4, D4bg, E4, E4bg, E4mt, F4, F4mt, F4sfm, F4tmb, L3XTG, Pi3, Pi3mrk, Pi3sbs. Course coordinator: Finn Lindgren, finn@maths.lth.se, Matematisk statistik. Recommended prerequisits: A basic course in mathematical statistics and, additionally, a course in Image analysis or at least one course in Markov processes or Stationary stochastic processes. Familiarity with Matlab. The course might be cancelled if the numer of applicants is less than 16. Assessment: Written and oral project presentation. Further information: The course is also given at the faculty of science with the code MASM13. Home page: http://www.maths.lth.se/matstat/kurser/fms150mas228/.

Aim
The aim of the course is to provide the student with tools for handling high-dimensional statistical problems, models, and methods, with practical applications, mainly image analysis and spatial statistics. Of special importance are the Bayesian aspects, since they form the foundation for a large part of the modern image analysis methods. These are, in the course, related to applications in remote sensing and environmental statistics.

Knowledge and understanding
For a passing grade the student must

• explain and use the concept of a stochastic model, in particular from a Bayesian perspective,

• describe the principles of Bayesian modelling and inference,

• identify and describe stochastic models and analysis methods for high-dimensional problems, in particular regarding image analysis and spatial statistics.

Skills and abilities
For a passing grade the student must

• independently suggest and analyse stochastic models for high-dimensional data, in particular in image analysis and spatial statistics,

• independently implement a computer program for the solution of a given statistical problem and relating analysis method,

• present motivations, course of action, and conclusions in the solution of a given statistical problem, both written and orally.

Judgement and approach
For a passing grade the student must

• identify and problemise possibilities and limitations of stochastic modelling and inference, in particular in high-dimensional problems,

• be able to assume a stochastic point of view on random variation in natural phenomena.

Contents
Bayesian methods for stochastic modelling, classification and reconstruction. Markov fields, Gibbs distributions, deformable templates, such as Snakes. Correlation structures, multivariate techniques, analysis of discrimination. Simulation methods for stochastic inference (MCMC, etc.). Stochastic remote sensing and spatial statistics.

Literature
Lindgren, F: Image Modelling and Estimation - A Statistical Approach, 2006.