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Photometric models in multispectral machine vision

The performance of several tasks in multispectral computer vision involves assumptions about the reflection of light from surfaces. These tasks include color constancy (visual representation of spectral reflectances independent of the illuminant spectrum), object-based image segmentation, and deduction of the shape of a surface from its shading. Most color-constancy theories implicitly assume Lambertian, coplanar reflecting surfaces, a distant viewer, and a distant light source that may have many components that are spatially and spectrally distinct. Object-based-segmentation theories allow curved surfaces, each of whose scattering kernels is the sum of a few separable terms (each of which is the product of a wavelength-dependent part and a geometry-dependent part). There is no restriction on the distances of light sources or observer. However, for these theories the illuminant angular/spectral distribution must consist of only one or two separable terms. Finally, A. Petrov's shape-from-shading theory allows the light source to have nearly arbitrary spectral and spatial composition, but requires the surface scattering kernels to have Lambertian dependence on the surface normal. The present paper compares these photometric models.