What are the distance metrics for local features?

Previous research has found that the distance metric for similarity estimation is determined by the underlying data noise distribution. The well known Euclidean(L2) and Manhattan (L1) metrics are then justified when the additive noise are Gaussian and Exponential, respectively. However, finding a suitable distance metric for local features is still a challenge when the underlying noise distribution is unknown and could be neither Gaussian nor Exponential. To address this issue, we introduce a modeling framework for arbitrary noise distributions and propose a generalized distance metric for local features based on this framework. We prove that the proposed distance is equivalent to the L1 or the L2 distance when the noise is Gaussian or Exponential. Furthermore, we justify the Hamming metric when the noise meets the given conditions. In that case, the proposed distance is a linear mapping of the Hamming distance. The proposed metric has been extensively tested on a benchmark data set with five state-of-the-art local features: SIFT, SURF, BRIEF, ORB and BRISK. Experiments show that our framework better models the real noise distributions and that more robust results can be obtained by using the proposed distance metric.