Approximate Correspondences in High Dimensions

Abstract

Pyramid intersection is an efficient method for computing an approximate partial matching between two sets of feature vectors. We introduce a novel pyramid embedding based on a hierarchy of non-uniformly shaped bins that takes advantage of the underlying structure of the feature space and remains accurate even for sets with high-dimensional feature vectors. The matching similarity is computed in linear time and forms a Mercer kernel. We also show how the matching itself (a correspondence field) may be extracted for a small increase in computational cost. Whereas previous matching approximation algorithms suffer from distortion factors that increase linearly with the feature dimension, we demonstrate thatour approach can maintain constant accuracy even as the feature dimension increases. When used as a kernel in a discriminative classifier, our approach achieves improved object recognition results over a state-of-the-art set kernel.