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Abstract: In this paper, the problem of indexing symbolic images based on spatial similarity is addressed. A model based on modified triangular spatial relationship (TSR) and B-tree is proposed. The model preserves TSR among the components in a symbolic image by the use of quadruples. A Symbolic Image Database (SID) is created through the construction of B-tree, an efficient multilevel indexing structure. A methodology to retrieve similar symbolic images for a given query image is also presented. The presented retrieval model has logarithmic search time complexity. The study made in this work reveals that the model bears various advantages when compared to other existing models and it could be extended towards dynamic databases. An extensive experimentation is conducted on various symbolic images and also on the ORL and YALE face databases. The results of the experimentation conducted have revealed that the proposed scheme outperforms the existing algorithms and is of practical relevance. [Copyright &y& Elsevier]

Abstract: In this paper, a novel method of representing symbolic images in a symbolic image database (SID) invariant to image transformations, useful for exact match retrieval is presented. The proposed model is based on Triangular Spatial Relationship (TSR) [Guru, D.S., Nagabhushan, P., 2001. Triangular spatial relationship: A new approach for spatial knowledge representation, Pattern Recognition Lett. 22, 999–1006]. The proposed model preserves TSR among the components in a symbolic image by the use of quadruples. A distinct and unique key called TSR key is computed for each distinct quadruple. The mean and standard deviation of the set of TSR keys computed for a symbolic image are stored along with the total number of TSR keys as the representatives of the symbolic image. An exact match retrieval scheme based on the modified binary search technique [Guru, D.S., Raghavendra, H.J., Suraj, M.G., 2000. An adaptive binary search based sorting by insertion: An efficient and simple algorithm, Statist. Appl., 2, 85–96] is also presented in this paper. The presented retrieval scheme requires O(log n) search time in the worst case, where n is the total number of symbolic images in the SID. An extensive experimentation on a large database of 13,680 symbolic images is conducted to corroborate the superiority of the model. [Copyright &y& Elsevier]

In this paper, an important aspect in creating a symbolic image database (SID), useful for exact match retrieval is addressed. The problem in conventional pairwise spatial relationships (particularly the 9DLT matrix) based approach for representing symbolic images in SID is discussed. An efficient method specifically for exact match retrieval, invariant to image transformations is proposed. In order to take care of image transformations, a new concept called direction of reference is introduced. The relative spatial relationships existing among the components present in an image are perceived with respect to the direction of reference and preserved by a set of triples. The proposed method is based upon principal component analysis (PCA). The first principal component vector (PCV) of the set of triples corresponding to an image is computed and stored as the representative of that image. The PCVs corresponding to n images to be archived in the SID are stored in a sorted order. A methodology for exact match retrieval is also presented in this paper. The presented retrieval algorithm takes O(logn) search time in the worst case, with the help of the binary search technique, where n is the number of symbolic images stored in the SID. [Copyright &y& Elsevier]