Image Similarity Assessment Based on Coefficients of Spatial Association

摘要

This paper focuses on the construction of image similarity indices that consider the hidden spatial association between two images. The proposal is a variant of a structural similarity (SSIM) coefficient and introduces a codispersion coefficient to capture the hidden spatial association between two images in a particular direction on a plane. The novel contribution of this article is the inclusion of the codispersion coefficient instead of the sample correlation coefficient. The difference between the codispersion and correlation coefficients is illustrated through two examples. We then show that this modified measure is a valid pseudo metric and has several useful properties, including quasi-convexity, which is established under very precise conditions. The quasi-convexity property is an attractive property that allows one to use this type of measure as a cost function in optimization problems. In addition, we introduce another variant of the SSIM with a contrast function that depends on the spatial lag on the space. This proposal trivially recovers the optimization properties of the SSIM. Various computational experiments with real datasets support our proposals and findings, and we characterize the practical advantages and drawbacks of the SSIM variants.