Color Retrieval in Vector Space Model

Many applications involving similarity search use the QBIC Euclidian distance to match two color histograms. To alleviate certain problems associated with this approach, which is based on a distance metric, in this paper, we propose a Color-Color Similarity Retrieval Approach to compute the similarities between images. This approach, based on the similarity matrix between feature vectors, leads to three new color-color similarity retrieval models, called (PA, Q), (P, QA), and (PB, QB) if the color-color similarity matrix A is positive definite. By precomputing the similarity matrix and all the products PA, PB, QA and QB, where P and Q are respectively, vectors representing images from the database and B is obtained by decomposing A in a special way, the retrieval function becomes linear during the retrieval step. To compute the similarity matrix A, we propose a more general form than that of the QBIC approach. In addition, in this paper, we introduce a new algorithm, Kernel Rocchio Algorithm, which combines the simplicity of Rocchio method with the power of non-linear kernel functions to improve the relevance feedback process. In this context, we prove that the proposed retrieval models are equivalent, in the sense that the query learned via relevance feedback in one model can also be learned in any of the other models. We implement our algorithms and test them on a synthetic dataset that allows easy mechanism for specification of image relevance for a user query. For learning purpose, we also consider a model that we refer to as the (P, Q) model, which does not require the use of the matrix A. Our results show that the (P, Q) retrieval model, used together with the polynomial kernel, provides better results compared to other combinations of retrieval models and kernel functions. We believe that if the method of computing color correlations is improved, the similarity retrieval model ((PA, Q), (P, QA), or (PB, QB)) should perform, quality-wise, just as well as the (P, Q) model, as shown by our theoretical results.