Heavy-Tailed Distances for Gradient Based Image Descriptors

Many applications in computer vision measure the similarity between images orimage patches based on some statistics such as oriented gradients. These are oftenmodeled implicitly or explicitly with a Gaussian noise assumption, leading tothe use of the Euclidean distance when comparing image descriptors. In this paper,we show that the statistics of gradient based image descriptors often followa heavy-tailed distribution, which undermines any principled motivation for theuse of Euclidean distances. We advocate for the use of a distance measure basedon the likelihood ratio test with appropriate probabilistic models that fit the empiricaldata distribution. We instantiate this similarity measure with the Gammacompound-Laplace distribution, and show significant improvement over existingdistance measures in the application of SIFT feature matching, at relatively lowcomputational cost.

Proceedings of the 25th Annual Conference on Neural Information Processing Systems (NIPS 2011), Granada, Spain

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