Approximate Correspondences in High Dimensions

Pyramid intersection is an efficient method for computing an approximate partial matching between two sets of feature vectors. We introduce a novel pyramid em- bedding 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. Whereas previous matching approxima- tion algorithms suffer from distortion factors that increase linearly with the fea- ture dimension, we demonstrate that our approach can maintain constant accuracy even as the feature dimension increases. When used as a kernel in a discrimina- tive classifier, our approach achieves improved object recognition results over a state-of-the-art set kernel.