Direct regularized surface reconstruction from gradients for Industrial Photometric Stereo

This paper addresses the issue of regularization in the surface reconstruction from gradients problem in Industrial Photometric Stereo. Regularization of the solution is a necessary step in an industrial environment, where algorithms must cope with non-Gaussian noise, such as outliers, or non-Lambertian textures such as corrosion. Introducing Tikhonov regularization into the global least squares solution suppresses the influence of outliers in the reconstruction. Viable methods should both minimize a global least squares cost function and also introduce some form of regularization into the solution; state-of-the-art methods to this end are grossly inefficient and are severely limited in the size of surface they can reconstruct. We present a new algorithm which can reconstruct a surface of 1200×1200, (i.e., greater than 1M-pixel) in a few seconds. This is orders of magnitude faster than state-of-the-art methods incorporating regularization, and hence presents the first method viable for regularized reconstructions in practical applications.