Hierarchical S(3)-coding of RGB histograms

Abstract

In this paper we introduce the representation theory of the symmetric group S (3) as a tool to investigate the structure of the space of RGB-histograms and to construct fast transforms suitable for search in huge image databases. We show that the theory reveals that typical histogram spaces are highly structured. The algorithms exploit this structure and construct a PCA like decomposition without the need to construct correlation or covariance matrices and their eigenvectors. A hierarchical transform is applied to analyze the internal structure of these histogram spaces. We apply the algorithms to two real-world databases (one from an image provider and one from a image search engine company) containing over one million images. © 2010 Springer-Verlag Berlin Heidelberg.