Estimating the Parameters of an Illumination Model Using Photometric Stereo

We investigate the accurate recording of an object's geometric and material properties using photometric stereo. This includes the simultaneous estimation of surface normals and surface reflectance parameters. We assume fairly general reflectance properties, including a combination of diffuse and specular reflection. By applying nonlinear regression techniques to a simplified version of the Torrance-Sparrow model we show how to do the simultaneous estimation in the presence of noise in such a way that any ill-conditioning or inadequacy of fit can be measured and detected. Thus, no smoothness or regularization assumptions need be made, and at all times an estimate of the accuracy of the obtained parameters is available. We also develop a criterion for making choices about those lighting setups that minimize ill-conditioning effects and maximize parameter precision. Finally, we eliminate the usual guesswork associated with parameter starting values by showing how to automatically obtain such values at each image pixel. The paper concludes with a number of examples of the method applied to simulations and real objects, followed by a discussion of the results together with suggestions for improvements to future systems.