An efficient and locality-oriented Hausdorff distance algorithm: Proposal and analysis of paradigms and implementations

Abstract

Hausdorff distance (HD) is a popular similarity metric used in the comparison of images or 3D volumes. Although popular, its main weakness is computing power consumption, being one of the slowest set distances. In this work, a novel, parallel and locality-oriented Hausdorff distance implementation is proposed. Novel as it is the first time in the literature that an actual algorithmic implementation using morphological dilations is proposed and thoroughly evaluated. Parallel, as it is more robust in terms of parallelization than the state-of-the-art algorithm and local as it has an intrinsic sensitivity to voxels that are closer in space. This proposal can be faster than the state-of-the-art in several practical cases such as in medical imaging registrations (up to 8 times faster on average in one of the CPU experiments) and is faster in the worst-case (up to 22337 times faster in one of the CPU experiments). Worst-case scenarios and high resolution volumes also favor the proposed approach. Throughout the work, several sequential and parallel CPU and GPU implementations are evaluated and compared.