Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)
Kristen Grauman, Trevor Darrell
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.