Convergence rate in terms of the continuous SSIM (cSSIM) index in RBF interpolation

The Structural Similarity index (SSIM) is a very popular tool for the evaluation of the similarity between two images. In this work, we extend it by introducing the continuous SSIM (cSSIM) index. Then, focusing on Radial Basis Function (RBF) interpolation, we provide theoretical results concerning the convergence rate of a RBF interpolant in terms of the cSSIM index. The theoretical findings are then confirmed by numerical experiments.