Maximum Likelihood Shape Matching

Many visual matching algorithms can be described in terms of the features and the inter-feature distance or metric. The most commonly used metric is the sum of squared differences (SSD), which is valid from a maximum likelihood perspective when the real noise distribution is Gaussian. However, we have found experimentally that the Gaussian noise distribution assumption is often invalid. This implies that other metrics, which have distributions closer to the real noise distribution, should be used. In this paper we considered a shape matching application. We implemented two algorithms from the research literature and for each algorithm we compared the efficacy of the SSD metric, the SAD (sum of the absolute differences) metric, and the Cauchy metric. Furthermore, in the case where sufficient training data is available, we discussed and experimentally tested a new metric based directly on the real noise distribution, which we denoted the maximum likelihood metric.