Interpreting the ratio criterion for matching SIFT descriptors

Abstract

Matching keypoints by minimizing the Euclidean distance between their SIFT descriptors is an effective and extremely popular technique. Using the ratio between distances, as suggested by Lowe, is even more effective and leads to excellent matching accuracy. Probabilistic approaches that model the distribution of the distances were found effective as well. This work focuses, for the first time, on analyzing Lowe’s ratio criterion using a probabilistic approach. We provide two alternative interpretations of this criterion, which show that it is not only an effective heuristic but can also be formally justified. The first interpretation shows that Lowe’s ratio corresponds to a conditional probability that the match is incorrect. The second shows that the ratio corresponds to the Markov bound on this probability. The interpretations make it possible to slightly increase the effectiveness of the ratio criterion, and to obtain matching performance that exceeds all previous (non-learning based) results.