Robust Surface Reconstruction

We propose a method to reconstruct surfaces from oriented point clouds corrupted by errors arising from range imaging sensors. The core of this technique is the formulation of the problem as a convex minimization that reconstructs the indicator function of the surface’s interior and substitutes the usual least-squares fidelity terms by Huber penalties to be robust to outliers, recover sharp corners, and avoid the shrinking bias of least-squares models. To achieve both flexibility and accuracy, we couple an implicit parametrization that reconstructs surfaces of unknown topology with three adaptive discretizations that avoid the high memory and computational cost of volumetric representations: two hierarchical B-spline bases of degree 1 and 2, and a dictionary of quadratic hierarchical B-splines. The hierarchical structure of the discretizations speeds minimization through multiresolution, while the proposed splitting algorithm minimizes non-differentiable functionals and is easy to parallelize. In experiments, our model improves reconstruction from synthetic and real data while the choice of discretization affects both the accuracy of the reconstruction and its computational cost.