Bayesian decision theory, the maximum local mass estimate, and color constancy

Abstract

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. AbstractVision 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 insucient use of structure in the posterior probability. The squared error penalty of the MMSE estimator does not reect typical penalties.We describe a new estimator, which we call maximum local mass (MLM) [10,26,65], which integrates the local probability density. The MLM method is sensitive to local structure of the posterior probability, which MAP is not. The new method uses an optimality criterion that is appropriate for perception tasks: it nds the most probable approximately correct answer. For the case of low observation noise, we provide an ecient approximation.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 method may prove useful in other vision problems as well.

Luminosity thresholds: effects of test chromaticity and ambient illumination

“…Recent computational approaches to color constancy, however, have employed Bayesian methods that incorporate probabilistic descriptions of which surfaces and illuminants are most likely to occur. 30,46,47 In the Bayesian context it is possible to make a reasonable estimate both of the relative spectral power distribution and of the overall illuminant intensity. 46,47 In practice, we modeled only the relative shape of the luminosity threshold surfaces.…”

“…30,46,47 In the Bayesian context it is possible to make a reasonable estimate both of the relative spectral power distribution and of the overall illuminant intensity. 46,47 In practice, we modeled only the relative shape of the luminosity threshold surfaces. For this reason the absolute intensity of the equivalent illuminant was undefined in our model fits.…”

Exploiting the generic viewpoint assumption

“…Generic variables could be estimated with coarse precision, and scene parameters with high precision. See [11,23,24,65] for examples of this approach. An advantage is that it avoids dividing the world parameters into two groups, generic variables and scene parameters.…”

“…[62] for a related non-Bayesian approach. Marginalization over the generic variables can also be interpreted using the loss functions of Bayesian decision theory [4], discussed in Section 4.2 and in [23, 65,24].…”

Color Constancy for Scenes with Varying Illumination

“…In a general context this problem has proven difficult to solve, so to make progress, restrictive assumptions are made. In particular, it is common to assume that the scene is flat [9,13,14], that the illumination is constant throughout [2,3,9,10,15], and that all reflectances are matte. Finlayson [8] has shown that if we focus on solving only for surface chromaticity and forego estimating surface lightness then the restriction to flat matte surfaces can be relaxed.…”