Surface Reconstruction from Gradient Fields Using Box-Spline Kernel

Surface reconstruction from gradient fields is of wide application in computer vision fields. Traditional methods usually enforce surface integrability in discrete domain, while current kernel approach suffers the problems of parameter choice. In this paper, we propose a novel method, i.e. kernel gradient regression, to reliably reconstruct surfaces. The box-spline kernel, instead of the common Gaussian kernel, is deployed in surface reconstruction due to its compact support and parameter robustness. To our knowledge, this is the first time to prove the special box-spline function as a new kind of positive definite spline kernel. The target surface is recovered under least-squares sense from the gradient fields, by converting the reconstruction problem to its kernel representation. Experimental results show that our proposed method outperform available approaches in preserving sharp edges and fine details, without prior knowledge of depth discontinuity.