Mathematical Optimization
in Graphics and Vision

Course Speakers:

Luiz Velho (IMPA)

Paulo Cezar Pinto Carvalho (IMPA)


Mathematical optimization have a fundamental importance for the solution of many problems in computer graphics and vision. This fact is apparent from a quick look at the SIGGRAPH proceedings, where a significant percentage of the papers employ in one way or another mathematical optimization techniques.

The course will provide a conceptual analysis of the problems in computer graphics and discuss the mathematical models used to solve them.This will motivate the audience to understand the importance of optimization techniques in graphics and vision.

The course will give an overview of combinatorial, continuous and variational optimization methods, focusing on graphical applications.


This tutorial course is divided into two parts. The first part will give a conceptual overview of computer graphics, focusing on problems and describing the mathematical models used to solve them. This is a short introduction to motivate the study of optimization techniques. The subject will be taught in such a way to make it clear the need to use optimization techniques in the solution of a large family of problems.

The second part will introduce the subject of optimization and provide a classification of the optimization problems into different categories: continuous, variational and combinatorial methods. Several examples in computer graphics will be given to illustrate each category of problems.

Course Notes

Course notes in PDF

Course Slides

Part 1: Optimization Problems in Graphics
Part 2: Overview of Optimization Techniques

Luiz Velho 2002-07-18