Inverting an Illumination Model from Range and Intensity Maps

We propose a solution to the problem of determining surface material properties from range and intensity data using a simplified version of the Torrance-Sparrow illumination model. The solution uses the photometric stereo method and regularization to invert the model equations at each point on a surface. Assuming a convex surface, one range map, and four or more intensity maps obtained using point light sources, we classify the surface into nonhighlight regions, specular highlight regions, and rank-deficient regions. This classification allows the appropriate solution method to be applied to each region. In nonhighlighted regions we use linear least squares, in highlight regions, nonlinear separable least squares with regularization, and in rank-deficient regions, interpolation. The solution consists of the values of the three parameters of the illumination model at each point on the surface. We believe this technique to be a useful adjunct to recently reported noncontact modeling systems. These systems have been designed to build computer graphics models automatically from real objects by determining surface geometry, surface relief texture, and material properties. Our technique greatly enhances the modeling of material properties. The paper concludes with a number of examples of the method applied to synthetic and real images, and a discussion of possibilities for future systems.