A Novel Algorithm for Computing Riemannian Geodesic Distance in Rectangular 2D Grids

We present a novel way to efficiently compute Riemannian geodesic distance over a two-dimensional domain. It is based on a previ- ously presented method for computation of geodesic distances on surface meshes. Our method is adapted for rectangular grids, equipped with a variable anisotropic metric tensor. Processing and visualization of such tensor fields is common in certain applications, for instance structure ten- sor fields in image analysis and diffusion tensor fields in medical imaging. The included benchmark study shows that our method provides signif- icantly better results in anisotropic regions and is faster than current stat-of-the-art solvers. Additionally, our method is straightforward to code; the test implementation is less than 150 lines of C++ code.