An efficient approach to directly compute the exact Hausdorff distance for 3D point sets

Abstract

Hausdorff distance measure is very important in CAD/CAE/CAM related applications. This manuscript presents an efficient framework and two complementary subalgorithms to directly compute the exact Hausdorff distance for general 3D point sets. The first algorithm of Nonoverlap Hausdorff Distance (NOHD) combines branch-and-bound with early breaking to cut down the Octree traversal time in case of spatial nonoverlap. The second algorithm of Overlap Hausdorff Distance (OHD) integrates a point culling strategy and nearest neighbor search to reduce the number of points traversed in case of spatial overlap. The two complementary subalgorithms can achieve a highly efficient and balanced result. Both NOHD and OHD compute the exact Hausdorff distance directly for arbitrary 3D point sets. We conduct a number of experiments on benchmark models and CAD application models, and compare the proposed approach with other state-of-the-art algorithms. The results demonstrate the effectiveness of our method.