Variational approach to interreflection in color images

Interreflections affect the colors of surfaces as they appear in images. The light reflected by one surface then impinges upon a second surface changes the color of the overall illumination that it receives and that 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.