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 o f the squared differences) metric is prevalent and justified from a maximum likelihood perspective when the additive noise distribution is Gaussian. B ased 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 r eal noise distribution, should be used. In this paper, we consider three di fferent applications: content-based retrieval in image databases, stereo ma tching, and motion tracking. In each of them, we experiment with different modeling functions for the noise distribution and compute the accuracy of t he methods using the corresponding distance measures. In our experiments, w e compared the SSD metric, the SAD (sum of the absolute differences) metric , the Cauchy metric, and the Kullback relative information. For several alg orithms from the research literature which used the SSD or SAD, we showed t hat greater accuracy could be obtained by using the Cauchy metric instead.