Bayesian Decision Theory, the Maximum Local Mass Estimate, and Color Constancy

Computational vision algorithms are often developed in a Bayesian framework. Two estimators are commonly used: maximum a posteriori (MAP), and minimum mean squared error (MMSE). We argue that neither is appropriate for perception problems. The MAP estimator makes insufficient use of structure in the posterior probability. The squared error penalty of the MMSE estimator does not reflect typical penalties. We apply this new estimator to color constancy. An unknown illuminant falls on surfaces of unknown colors. We seek to estimate both the illuminant spectrum and the surface spectra from photosensor responses which depend on the product of these unknown spectra. In simulations, we show that the MLM method performs better than the MAP estimator, and better than two standard color constancy algorithms. The MLM estimate may prove useful in other vision problems as well. IEEE Intl. Conf. on Computer Vision, Cambridge, MA, June, 1995 This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c ©Mitsubishi Electric Research Laboratories, Inc., 1995 201 Broadway, Cambridge, Massachusetts 02139