## COMP 790-098: Optimal Estimation in Image Analysis

**Spring 2016, Mon/Wed 2:30pm-3:45pm, SN 284**

**Instructor: Marc Niethammer****Email:** (mn -at- cs.unc.edu)**Phone:** 919-590-6149**Office: **219 Sitterson Hall

## Overview

The amount of image data obtained from standard cameras, microscopes, ultrasound or magnetic resonance scanners is ever increasing. This makes image analysis (the automatic extraction of quantitative information from such data) essential. While a huge number of algorithms exist to tackle problems ranging from image segmentation, image registration, to 3D scene reconstruction, many of these algorithms require the formulation and solution of similar optimization problems.

The focus of this course is therefore to introduce students to the basic approaches in formulating and solving such optimization problems. The course will be split in three parts: (i) background material in numerical optimization, (ii) continuous formulations, and (iii) discrete formulations of optimization problems in image analysis. Special emphasis will be given to numerical solution methods for example problems.

**Prerequisites:** The material covered will be diverse. Prior exposure to all the relevant topics is therefore unrealistic. Consequentially, the course lecture will be supplemented with background material as needed. Focus will be on the understanding of the overall concepts in the context of image analysis. Exposure to standard probability theory, basics of differential equations, and an overall interest in mathematical problem formulations will be a sufficient background.

**Format:** The course will combine standard lectures as well as paper and project presentations.

**Resources:** There is no standard textbook covering the material of this course and a textbook is therefore not required. Related conference and journal articles will be provided through Sakai. Further, I will make use of material from the following books (some of them available freely or electronically at UNC -- as indicated):

1. | Geometric Partial Differential Equations and Image Analysis | by Guillermo Sapiro |

2. | Level Set Methods and Dynamic Implicit Surfaces | by Stanley Osher and Ronald Fedkiw |

3. | Finite Difference Schemes and Partial Differential Equations | by John Strikwerda |

4. | Numerical Recipes in C (available at http://www.nr.com/) | by William H. Press et al. |

5. | Markov Random Field Modeling in Image Analysis (available as an electronic resource from the UNC library) | by Stan Z. Li |

6. | Numerical Optimization (available as an electronic resource from the UNC library) | by Nocedal/Wright |

7. | Convex Optimization (available at http://www.stanford.edu/~boyd/cvxbook/) | by Boyd/Vandenberghe |

8. | The Elements of Statistical Learning (available at http://statweb.stanford.edu/~tibs/ElemStatLearn/ ) | by Hastie/Tibshirani/Friedman |

**Lecture materials will be posted on Sakai**

**Grading:** The course grade will be based on: (i) a set of homework assignment (theory + implementation); (ii) presentation of a research paper or related background material; (iii) a final project related to the course subject.