Tolerance Satisfiability Sequences for Image Similarity

We propose a solution to a fundamental problem of content based image retrieval (CBIR), "How to calculate the degree of similarity among a pair of images". This article introduces a novel technique called Tolerance Satisfiablity Sequence (TSS) which is based on the concept of tolerance space and near set theory. In this work, images are divided into different visual element (objects) and affinity is calculated between the corresponding object of the two images. Each object is further divided into sub-objects that are mapped to each other under the constraints of tolerance satisfiability. The maximal satisfying set of sub objects (between the two parent objects) is found. This maximal set of sub-object is (termed as TSS) compared with the parent object i.e. the ratio of the cardinality of maximum satisfying set to the cardinality of the parent object is calculated and this gives the quantified similarity index termed as Tolerant Satisfiable Similarity Metric (TSSM). Initially, we verified that proposed approach is metric as well as pseudo-metric and later it is compared with popular image nearness metrics, viz., Hausdorff and Structural Similarity Index (SSIM). It is experimentally proved that the TSSM outperformed them in visual acuity.