Fast Marching farthest point sampling

Abstract

We introduce the Fast Marching farthest point sampling (FastFPS) approach for the progressive sampling of planar domains and curved manifolds in triangulated, point cloud or implicit form. By using Fast Marching methods 2 , 3, 6 for the incremental computation of distance maps across the sampling domain, we obtain a farthest point sampling technique superior to earlier point sampling principles in two important respects. Firstly, our method performs equally well in both the uniform and the adaptive case. Secondly, the algorithm is applicable to both images and higher dimensional surfaces in triangulated, point cloud or implicit form. This paper presents the methods underlying the algorithm and gives examples for the processing of images and triangulated surfaces. A companion report 4 provides details regarding the application of the FastFPS algorithm to point clouds and implicit surfaces.