Prior model evaluation from Null Space Compensation perspective with application to surface reconstruction from single images

Abstract

Prior model is widely applied in the area of computer vision and computer graphics. However, there is still a lack of a general theoretical scheme for evaluating the performance of the priors and a guidance for choosing suitable models. In this paper, a general scheme is proposed for linear singular problems based on the idea of Null Space Compensation. It is proved that for a linear prior model the principal directions obtained from the singular value decomposition of the model shall not be parallel to those of the system matrix determined by the problem. It is also suggested that for a nonlinear prior, higher correlation between the null space components of the estimate data based on the given prior and those of the ground truth or controlled data indicate the better suitability of the prior. The proposed evaluation scheme is demonstrated through an application to a linearized shape from shading problem, where surface shall be reconstructed from single 2D images. Both linear model and nonlinear constraints are evaluated with experiments on both synthetic images and real images. The results validate the proposed evaluation scheme and its capability for guiding in choosing a good prior model structure.