Toward improved ranking metrics

In many computer vision algorithms, a metric or similarity measure is used to determine the distance between two features. The Euclidean or SSD (sum of the squared differences) metric is prevalent and justified from a maximum likelihood perspective when the additive noise distribution is Gaussian. Based on real noise distributions measured from international test sets, we have found 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 consider three different applications: content-based retrieval in image databases, stereo matching, and motion tracking. In each of them, we experiment with different modeling functions for the noise distribution and compute the accuracy of the methods using the corresponding distance measures. In our experiments, we compared the SSD metric, the SAD (sum of the absolute differences) metric, the Cauchy metric, and the Kullback relative information. For several algorithms from the research literature which used the SSD or SAD, we showed that greater accuracy could be obtained by using the Cauchy metric instead.