An efficient computational algorithm for Hausdorff distance based on points-ruling-out and systematic random sampling

This paper proposes a novel algorithm for fast and accurate Hausdorff distance (HD) computation. The Hausdorff distance is used to measure the similarity between two point sets in various applications. However, it is hard to compute the HD algorithm efficiently between very large-scale point sets while ensuring the accuracy of the HD. The directed HD algorithm has two loops (called the outer loop and the inner loop) for calculating MAX-MIN distance, and the state-of-the-art algorithms, such as the Early break method and the Diffusion search method, focused on reducing the iterations of the inner loop. Our algorithm, however, concentrates on reducing the iterations of the outer loop. The proposed method simultaneously computes the temporary HD and temporary minimum distances of points corresponding to the outer loop using the opposite HD computation with very small systematic samples. Thereafter, a strategy of ruling out is employed to exclude non-contributing points. The new approach reduces the problems of different grid sizes and highly overlapping point sets as well as the very large-scale point sets. 3-D point clouds and real brain tumor segmentation (MRI 3-D volumes) are used for comparing the performance of the proposed algorithm and the state-of-the-art HD algorithms. In experimental results with 3-D point clouds, the proposed method is more than at least 1.5 times as faster as the compared algorithms. And, in experimental results with MRI 3-D volumes, the proposed method achieves a better performance than the compared algorithms over all pairs regardless of the grid size. Thus, as a whole, the proposed algorithm outperforms the compared algorithms.