An invariant scheme for exact match retrieval of symbolic images: Triangular spatial relationship based approach

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.