Authors:
Reiner Lenz
1
and
Pedro Latorre Carmona
2
Affiliations:
1
ITN, Sweden
;
2
Universidad Jaume I Campus del Riu Sec s/n, Spain
Keyword(s):
RGB-Histograms, Image Databases, Finite Groups, Harmonic Analysis.
Related
Ontology
Subjects/Areas/Topics:
Computer Vision, Visualization and Computer Graphics
;
Feature Extraction
;
Features Extraction
;
Image and Video Analysis
;
Informatics in Control, Automation and Robotics
;
Signal Processing, Sensors, Systems Modeling and Control
;
Statistical Approach
Abstract:
In this paper we introduce the representation theory of the symmetric group~$ SPG$ as a tool to investigate the structure of the space of $RGB$-histograms. We show that the theory reveals that typical histogram spaces are highly structured and that these structures originate partly in group theoretically defined symmetries. The algorithms exploit this structure and constructs a PCA like decomposition without the need to construct correlation or covariance matrices and their eigenvectors. We implemented these algorithms and investigate their properties with the help of two real-world databases (one from an image provider and one from a image search engine company) containing over one million images.