Relative Spatial Distance Matrix: a Novel and Invariant Data Structure for Representation and Retrieval of Exact Match Symbolic Images

This paper proposes a new data structure called relative spatial distance (RSD) matrix, useful for the representation of symbolic images. RSD matrix is constituted by the relative spatial distances between the iconic objects in the symbolic image. A set of triplets constituted by the pair -wise relative spatial distances between iconic objects forms the surrogate representation of the symbolic image. In order to reduce the space complexity of the representation scheme, a unique one-to-one mapping function is devised to map each triplet uniquely onto real space as key values. The mean and standard deviations of these unique keys in the real space along with number of iconic objects consisted by the symbolic image, forms the final representation vector of the symbolic image. A symbolic image database (SID) is created by storing the representative vectors of images under consideration in sorted order. An SID having 8372 instances of symbolic images is considered for experimentation, to validate the integrity and accuracy of the proposed work. Modified binary search [11] of complexity O(logn) is employed to retrieve the exact match images from the SID.