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.

本文提出了一种新的算法，用于快速，准确的Hausdorff距离（HD）计算。Hausdorff距离用于测量各种应用中两个点集之间的相似度。但是，很难在非常大的点集之间有效地计算HD算法，同时又要确保HD的准确性。定向高清算法具有两个循环（称为外循环和内循环），用于计算MAX-MIN距离，而最新算法（如Early Break方法和Diffusion搜索方法）专注于减少内循环的迭代。但是，我们的算法专注于减少外循环的迭代。所提出的方法使用具有非常小的系统样本的相反的HD计算，同时计算与外环相对应的点的临时HD和临时最小距离。此后，采用排除策略来排除非贡献点。新方法减少了不同的网格大小和高度重叠的点集以及非常大的点集的问题。3-D点云和真实脑肿瘤分割（MRI 3-D卷）用于比较所提出算法和最新HD算法的性能。在具有3-D点云的实验结果中，该方法的速度至少是比较算法的1.5倍以上。而且，在MRI 3-D体积的实验结果中，无论网格大小如何，所提出的方法在所有对中都比比较算法具有更好的性能。因此，总体上，所提出的算法优于所比较的算法。