Implicit surface reconstruction with total variation regularization

Implicit representations have been widely used for surface reconstruction on account of their capability to describe shapes that exhibit complicated geometry and topology. However, extra zero-level sets or spurious sheets usually emerge in implicit algorithms and damage the reconstruction results. In this paper, we propose a reconstruction approach that involves the total variation (TV) of the implicit representation to minimize the occurrence of spurious sheets. Proof is given to show that the recovered shape has the simplest topology with respect to the input data. By using algebraic spline functions as the implicit representation, an efficient discretization is presented together with effective algorithms to solve it. Hierarchical structures with uniform subdivisions can be applied in the framework for fitting fine details. Numerical experiments demonstrate that our algorithm achieves high quality reconstruction results while reducing the existence of extra sheets.