Toward Robust Distance Metric Analysis for Similarity Estimation

In this paper, we present a general guideline to establish the relation between a distribution model and its corresponding similarity estimation. A rich set of distance metrics, such as harmonic distance and geometric distance, is derived according to Maximum Likelihood theory. These metrics can provide a more accurate feature model than the conventional Euclidean distance (SSD) and Manhattan distance (SAD). Because the feature elements are from heterogeneous sources and may have different influence on similarity estimation, the assumption of single isotropic distribution model is often inappropriate. We propose a novel boosted distance metric that not only finds the best distance metric that fits the distribution of the underlying elements but also selects the most important feature elements with respect to similarity. We experiment with different distance metrics for similarity estimation and compute the accuracy of different methods in two applications: stereo matching and motion tracking in video sequences. The boosted distance metric is tested on fifteen benchmark data sets from the UCI repository and two image retrieval applications. In all the experiments, robust results are obtained based on the proposed methods.