Robust polynomial texture mapping for shadow and specularity interpolation

PTM forms an alternative method for apprehending surface properties that extends a simple model of image formation from the Lambertian variant of PST to more general reflectances. Here we consider solving such a model in a robust version using either LMS or LTS, which is useful in the identification of matte, shadow and specularity automatically. Identifying the matte contribution, we can then estimate chromaticity and surface properties accurately. We can model specular and non-specular contributions using two sets of RBF regression over specular and non-specular pixels. Then for a new lighting direction, we can interpolate both specularity and shadows. Finally, to generate the full color output we can either utilize the estimated chromaticity along with specular chromaticity, or model specularity and shadow for each color channel separately. The latter is found to generate qualitatively and quantitatively better results. Overall, the proposed approach generates convincing interpolations of both specularities and shadows.