Fast retrieval of color objects with multidimensional orthogonal polynomials

In this paper, a color model for the Orthogonal Polynomials Transform and modifications to the generating function of the transform's coefficients in order to enhance the speed of the transform have been proposed. Utilizing this simple and integer-based transform, a fast color image annotation and retrieval system is proposed. In the proposed retrieval system, images are represented as a mixture of Gaussians which are built from the transform's partial coefficients. Annotation is performed by estimating the Kullback Leibler distance between the Gaussian distributions of the query and that of the database. This retrieval system is fast owing to the following reasons: 1) Usage of a computationally light transform 2) Sufficiency of partial decoding of the transform's coefficients for building the image representation owing to its energy compaction property 3) Exploitation of the inherent symmetry of the point spread operator of transform which is useful for fast determination of the transform's coefficients and 4) Non-usage of any time consuming weight assignment algorithm while fusing multiple features into the feature vector. The algorithm is validated on the COIL-100 database which has been categorized into six types for the purpose of analyzing the results better. An optimum number of extracted features and Gaussian mixtures that give a good annotation and retrieval performance is determined. The performance of the proposed system is compared with that of other recent compressed domain techniques and also with the feature set given by the local descriptors of SIFT.