Distributions of local radius indices on periodic tessellations

This paper presents a theoretical analysis of a newly proposed texture similarity feature, Local Radius Index (LRI). LRI is designed to enable texture similarity metrics consistent with human perception to be based on it, and has been successfully applied in several applications, including perceptual image compression, identical texture retrieval and texture classification. In this paper, a theoretical analysis of its different versions, LRI-A and LRI-D, is presented for textures modeled as periodic tessellations. General formulas are derived to predict LRI-A and LRI-D feature vectors, which are histograms. The analysis reveals the fundamental relationship between LRI-A and LRI-D. Numerical results demonstrate the accuracy of the analysis.