Regularization: Problems and Promises

Boult, Terrance E.

Regularization is becoming a popular framework for describing and solving many ill-posed problems of computer vision. Of course, a generalized framework is only useful if it provides additional insights or benefits unavailable without it. This paper discusses some of the benefits promised by the regularization framework. Additionally, as a mathematical paradigm for vision, regularization presents many difficulties for the vision researcher, and some of these difficulties are discussed in this paper. The paper then discusses the lack of development of most of the "promises of regularization" theory, and gives a. brief look as some of the promises which have been realized. In the context of smooth surface reconstruction, the paper addresses one of the most difficult problems with the use of regularization: the problem of determining an appropriate functional class, norm, and regularization stabilizing functional. In particular, results are discussed from an experiment which subjectively orders various functional classes and stabilizing functionals for a regularization-based formulation of the surface reconstruction problem. The conclusions drawn include the fact that there exist non-traditional formulations of this regularization problem which provide better results. The paper concludes with a brief mention of two more general frameworks and their relationship to regularization.



More About This Work

Academic Units
Computer Science
Department of Computer Science, Columbia University
Columbia University Computer Science Technical Reports, CUCS-321-88
Published Here
December 7, 2011