Discontinuity-preserving Normal Integration with Auxiliary Edges

Many surface reconstruction methods incorporate normal integration which is a process to obtain a depth map from surface gradients. In this process the input may represent a surface with discontinuities e.g. due to self-occlusion. To reconstruct an accurate depth map from the input normal map hidden surface gradients occurring from the jumps must be handled. To model these jumps correctly we design a novel discretization for the domain of normal integration. Our key idea is to introduce auxiliary edges which bridge between piecewise-smooth planes in the domain so that the magnitude of hidden jumps can be explicitly expressed on finite elements. Using the auxiliary edges we design a novel algorithm to optimize the discontinuity and the depth map from the input normal map. Our method optimizes discontinuities by using a combination of iterative re-weighted least squares and iterative filtering of the jump magnitudes on auxiliary edges to provide strong sparsity regularization. Compared to previous discontinuity-preserving normal integration methods which model the magnitude of jumps only implicitly our method reconstructs subtle discontinuities accurately thanks to our explicit representation allowing for strong sparsity regularization.