Noise reduction in surface reconstruction from a given gradient field

We present a gradient space technique for noise reduction in surfaces reconstructed from a noisy gradient field. We first analyze the error sources in the recovered gradient field of a surface using a three-image photometric stereo method. Based on this analysis, we propose an additive noise model to describe the errors in the surface gradient estimates. We then use a vector space formulation and construct a multiscale orthonormal expansion for gradient fields. Using the sparse representation properties of this expansion, we develop techniques for reducing the gradient field noise by coefficient selection with thresholding. The simulation results indicate that the proposed technique provides significant improvement on the noise levels of both the estimated gradient fields and the reconstructed surfaces under heavy noise levels. Furthermore, the experiments using noisy photometric stereo image triplets of real range data suggest that the additive model remains viable after the nonlinear photometric stereo operation to provide accurate noise removal.