Monte Carlo evaluation of the Hausdorff distance for shape matching

In this work, we present a Monte Carlo approach to compute Hausdorff distance for locating objects in real images. Objects are considered to be only under translation motion. We use edge points as the features of the model. Using a different interpretation of the Hausdorff distance, we show how image similarity can be measured by using a randomly sub-sampled set of feature points. As a result of computing the Hausdorff distance on smaller sets of features, our approach is faster than the classical one. We have found that our method converges toward the actual Hausdorff distance by using less than 20 % of the feature points. We show the behavior of our method for several fractions of feature points used to compute Hausdorff distance. These tests let us conclude that performance is only critically degraded when the subsampled set has a cardinality under 15 % of the total feature points in real images.