Robust estimation of surface properties and interpolation of shadow/specularity components

The Polynomial Texture Map framework (PTM) extends the simple model of image formation from the Lambertian variant of Photometric Stereo (PST) to more general reflectances and to more complex-shaped surfaces. It forms an alternative method for apprehending object colour, albedo, and surface normals. Here we consider solving such a model in a robust version, not to date attempted for PTM, with the upshot that both shadows and specularities are identified automatically without the need for any thresholds. Instead of the linear model used in few-source PST for Lambertian surfaces, PTM adopts a higher degree polynomial model. PTM has two aims: interpolation of images for new lighting directions, and recovery of surface properties. Here we show that a robust approach is a good deal more accurate in recovering surface properties. For new-lighting interpolation, we demonstrate that a simple radial basis function interpolation can accurately interpolate specularities as well as attached and cast shadows even with a medium-sized image set, with no need for reflectance sharing across pixels or extremely large numbers of interpolation coefficients.