Variational approach to interreflection in color images

Interreflections affect the colors of surfaces as they appear in images. The light reflected by one surface that then impinges upon a second surface changes the color of the overall illumination that it receives and hence the color of the light that it reflects. Both the relative colors and positions of the two surfaces affect the result. We analyze the physics of the interreflection process and extract constraints on the possible surface reflectances, ambient illumination, and geometric configuration of the surfaces. By using the calculus of variations, a finite-dimensional model of reflectance, and a one-bounce model of interreflection, we express these constraints as a set of equations that are then solved for the surface spectral reflectance functions of the surfaces, the spectrum of the ambient illumination, and local interreflection factors related to the scene geometry. The interreflection factors express how the image is altered by interreflection effects and can be used to produce an image shaded as it would appear had there been no interreflection; the surface reflectance functions provide color constancy. Although it is more complex than some previous analyses of interreflection, the variational approach is more general and relaxes some restrictive assumptions concerning the type of illumination and the number of surfaces. 1

Diagonal Transforms Suffice For Color Constancy:Proceedings of the Fourth International Conference on Computer Vision

The main result is to show that under the conditions imposed by the Maloney-Wandell color constancy algorithm, color constancy can be expressed in terms of a simple independent adjustment of the sensor responses, so long as the sensor space is first transformed to a new basis. The overall goal is to present a theoretical analysis connecting many established theories of color constancy. For the case where surface reflectances are two-dimensional and illuminants are three-dimensional, it is proved that perfect color constancy can always be solved for by an independent adjustment of sensor responses, which means that the color constancy transform can be expressed as a diagonal matrix. In addition to purely theoretical arguments, results from simulations of diagonal-matrix-based color constancy, in which the spectra of real illuminants and reflectances along with the human cone sensitivity functions were used, are presented. The simulations demonstrate that when the cone sensor space is transformed to its new basis in the appropriate manner, a diagonal matrix supports close to optimal color constanc