Fast Near-duplicate Image Detection in Riemannian Space by a Novel Hashing Scheme

Abstract

There is a steep increase in data encoded as symmetric positive definite (SPD) matrix in the past decade. The set of SPD matrices forms a Riemannian manifold that constitutes a half convex cone in the vector space of matrices, which we sometimes call SPD manifolds. One of the fundamental problems in the application of SPD manifolds is to find the nearest neighbor of a queried SPD matrix. Hashing is a popular method that can be used for the nearest neighbor search. However, hashing can't be directly applied to SPD manifolds due to its non-Euclidean intrinsic geometry. Inspired by the idea of kernel trick, a new hashing scheme for SPD manifolds by random projection and quantization in expanded data space is proposed in this paper. Experimental results in large scale near-duplicate image detection show the effectiveness and efficiency of the proposed method.