Efficient robust image interpolation and surface properties using polynomial texture mapping

Polynomial Texture Mapping (PTM) uses a simple polynomial regression to interpolate, and hence relight, image sets taken from a fixed camera but with multiple, changing lights with each light illuminating the scene in turn from different directions [1]. PTM is basically an extension of the simple Lambertian model of Photometric Stereo (PST), but replacing a linear term in the lighting direction vector by a polynomial. The advantage, and hence wide use, of PTM is that it provides some effectiveness in interpolating appearance including more complex phenomena such as interreflections, specularities and shadowing. As well as appearance modelling, PTM provides estimates of surface properties, i.e., chromaticity, albedo and surface normals. The most accurate model to date utilizes robust multivariate regression to generate a basic matte model, followed by Radial Basis Function (RBF) interpolation to give accurate interpolants of appearance. Using the original dimension of 6-coefficient PTM, but with robust identification of specular and shadow outliers, the underlying matte model has been shown to yield accurate surface properties. However, robust multivariate modelling is slow. Here we show that one can produce good quality appearance interpolants, plus accurate surface properties using PTM before the additional RBF stage, provided one increases the dimensionality beyond 6-D, and provided one still uses robust regression. However, here we show that the robust regression can find acceptably accurate inlier sets using a much less burdensome robust 1-D “location finder” (or “mode-finder”), rather than having to use robust multivariate processing. Moreover we show that, in contrast to current