An Introduction to Optimization Techniques in Computer Graphics

Abstract

Background Many students in Computer Science do not have a sufficient background in applied mathematics to employ state-of-the-art optimization techniques and to judge the outcome of such techniques critically (e.g. regarding the stability/quality/accuracy of their output). At the same time, the use of optimization techniques in computer graphics is becoming ubiquitous. Treating optimization algorithms as a black box yields sub-optimal results at best. At worst, stability issues and convergence problems may prevent the solution of a problem or impede the general application of a method to a wide range of input, i.e. beyond the set of examples shown in a paper. The course will draw attention to these aspects and to current best practices. This will enable participants to judge articles that use optimization schemes critically and improve their own skill set. Scope and Intended Audience For this purpose, we propose an introductory course on optimization techniques in computer graphics. We aim at thoroughly covering the basic techniques in optimization, only requiring a good working knowledge of the mathematical foundations in a standard CS curriculum, in particular, multi-dimensional analysis and linear algebra. Part of the course will be suitable for a starting PhD student. On the other end, our goal is to lead up to current research including modern ideas such as compressed sensing, convex variational formulations, and sparsity-inducing norms. We aim at exposing the major underlying ideas, exposing the working principles and giving hints for a successful implementation. The course thus also caters to the experienced researcher that seeks to utilize these modern techniques. We approach these goals by discussing a mixture of classic and more modern optimization approaches. Each section is presented by an expert in the area. Further, each section is comprised of two major parts: 1.) a condensed introduction of the necessary background and 2.) its application in particular graphics problems. We aim at giving implementation hints and the exposure of current-best-practices.