Which ranking metric is optimal? With applications in image retrieval and stereo matching

Euclidean metric is frequently used in computer vision, mostly ad-hoc without any justification. However we have found that other metrics like a double exponential or Cauchy metric provide better results, in accordance with the maximum likelihood approach. In this paper we experiment with different modeling functions for similarity noise and compute the accuracy of different methods using these modeling functions in two kinds of applications: content-based image retrieval from a large database and stereo matching. We provide a way to determine the modeling distribution which fits best the similarity noise distribution according to the ground truth. In the optimum case, when one has chosen the best modeling distribution, its corresponding metric will give the best ranking results for the ground truth provided.