Principal components analysis and neural network implementation of photometric stereo

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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

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