Abstract

How does shape-from-shading proceed when two or more different1 colored light sources are present? For a uniformly co&ied Lambertian surface illuminated by a collection of oint or extended light sources or interreflections, wit [ unknown directions and strengths, illumination varies spectrally with orientation from the surface. If light varies enou h in color and direction, then surface orientation can%, recovered by a kind of photometric stereo, but with a single image and many unknown li hts. RGB values lie on an ellipsoid in color space and fhe strengths and directions of three effective ‘lights ” can be recovered from regression and by additional constraints derived from three estimates of light source tilt. However, it is quite likely that illumination color does not var enough. In that case RGB points fill a lanar 2D elzpse in color s ace. Here we give a result For the elli se boundary tiat enables one to recover the strengtis and an le between two effective lights producing the. 2D sha%ing. We then show that equations for the tilts of the linearly related three effective lights in 3D give an additional three independent constraints. Solving yields lights in 2D and hence in 3D as well. Thus the rank-2 orientation-from-color problem reduces to known-light 2-image photometric stereo. Robust methods are used throughout. 1

Citations