Principal components analysis and neural network implementation of photometric stereo

An implementation of photometric stereo is described in which all directions of illumination are close to the viewing direction. This has practical importance but creates a numerical problem that is ill-conditioned. Ill-conditioning is dealt with in two ways. First, many more than the theoretical minimum number of required images are acquired. Second, principal components analysis (PCA) is used as a linear preprocessing technique to extract a reduced dimensionality subspace to use as input. Overall, the approach is empirical. The ability of a radial basis function (RBF) neural network to do non-parametric functional approximation is exploited. One network maps image irradiance to surface normal. A second network maps surface normal to image irradiance. The two networks are trained using samples from a calibration sphere. Comparison between the actual input and the inversely predicted input is used as a confidence estimate. Results on real data are demonstrated