Practical Least Squares for Computer Graphics

Abstract. The course presents an overview of the least-squares technique and its variants. A wide range of problems in computer graphics can be solved using the leastsquares technique (LS). Many graphics problems can be seen as finding the best set of parameters for a model given some data. For instance, a surface can be determined using data and smoothness penalties, a trajectory can be predicted using previous information, joint angles can be determined from end effector positions, etc. All these problems and many others can be formulated as minimizing the sum of squares of the residuals between some features in the model and the data. Despite this apparent versatility, solving problems in the least-squares sense can produce poor results. This occurs when the nature of the problem error does not match the assumptions of the least-squares method. The course explains these assumptions and show how to circumvent some of them to apply LS to a wider range of problem. The focus of the course is to provide a practical understanding of the techniques. Each technique will be explained using the simple example of fitting a line through data, and then illustrated through its use in one or more computer graphics papers. Prerequisites. The attendee is expected to have had an introductory course to computer graphics and some basic knowledge in linear algebra at the level of OpenGL transforms. Updates and Slides. The latest version of these notes and the associated slides are located a