Direct Solution of Orientation-from-Color Problem Using a Modification of Pentland's Light Source Direction Estimator

If a uniformly colored Lambertian surface is illuminated by a collection of point or extended light sources or interreflections, with unknown directions and strengths, such that illumination varies spectrally with orientation from the surface, then surface normals can be recovered up to an orthogonal transformation using a robust regression on points in color space. Recently, it was shown that the unknown orthogonal transformation can be recovered by applying an integrability condition on the recovered normals. However, the integrability method results in an unavoidable convex/concave ambiguity additional to the usual one. Here a much simpler method is set out that avoids this ambiguity. Using Pentland's or a similar tilt estimator for each of the RGB channels in turn, in effect treating the combination of lights as three single sources, the robust color space regression leads to three constraints on the slants of the three sources. The result is accurate recovery of light source directions and hence of surface normals. A self-check mechanism for evaluating the algorithm's performance on real images is introduced.