A new algorithm for computing the minimum Hausdorff distance between two point sets on a line under translation

To determine the similarity of two point sets is one of the major goals of pattern recognition and computer graphics. One widely studied similarity measure for point sets is the Hausdorff distance. So far, various computational methods have been proposed for computing the minimum Hausdorff distance. In this paper, we propose a new algorithm to compute the minimum Hausdorff distance between two point sets on a line under translation, which outperforms other existing algorithms in terms of efficiency despite its complexity of O((m+n)lg(m+n)), where m and n are the sizes of two point sets.