Fast and Accurate Redistancing by Directional Optimization

A fast and accurate algorithm for the reinitialization of the signed distance function in two and three spatial dimensions is presented. The algorithm has computational complexity $O(N \log N)$ for the reinitialization of $N$ grid points. The order of accuracy of the reinitialization is demonstrated to depend primarily on the interpolation algorithm used. Bicubic interpolation is demonstrated to result in fourth-order accuracy for smooth interfaces. Simple numerical examples demonstrating the convergence and computational complexity of the reinitialization algorithm in two and three dimensions are presented as verification of the algorithm.