Fast Marching farthest point sampling for implicit surfaces and point clouds

In a recent paper [13], the Fast Marching farthest point sampling strategy (FastFPS) for planar domains and curved manifolds was introduced. The version of FastFPS for curved manifolds discussed in the paper [13] deals with surface domains in triangulated form only. Due to a restriction of the underlying Fast Marching method, the algorithm further requires the splitting of any obtuse into acute triangles to ensure the consistency of the Fast Marching approximation. In this paper, we overcome these restrictions by using Mémoli and Sapiro’s [11, 12] extension of the Fast Marching method to the handling of implicit surfaces and point clouds. We find that the extended FastFPS algorithm can be applied to surfaces in implicit or point cloud form without the loss of the original algorithm’s computational optimality and without the need for any preprocessing.