Robust estimation of distance between sets of points

• Robust nearest neighbor distance distributions are computed through Monte Carlo.
• These are operated to get distributions of the average, minimum and maximum distances.
• Different tests are used to compare the measures wrt. values obtained by chance.
• The method is appropriate for problems that can be modeled through point processes.

This paper proposes a new methodology for computing Hausdorff distances between sets of points in a robust way. In a first step, robust nearest neighbor distance distributions between the two sets of points are obtained by considering reliability measures in the computations through a Monte Carlo scheme. In a second step, the computed distributions are operated using random variables algebra in order to obtain probability distributions of the average, minimum or maximum distances. In the last step, different statistics are computed from these distributions. A statistical test of significance, the nearest neighbor index, in addition to the newly proposed divergence and clustering indices are used to compare the computed measurements with respect to values obtained by chance. Results on synthetic and real data show that the proposed method is more robust than the standard Hausdorff distance. In addition, unlike previously proposed methods based on thresholding, it is appropriate for problems that can be modeled through point processes.