A nonparametric-test-based structural similarity measure for digital images

In image processing, image similarity indices evaluate how much structural information is maintained by a processed image in relation to a reference image. Commonly used measures, such as mean squared error (MSE) and peak signal to noise ratio (PSNR), ignore the spatial information (e.g. redundancy) contained in natural images, which can lead to an inconsistent similarity evaluation from the human visual perception. Recently, a structure similarity measure (SSIM), that quantifies image fidelity through estimation of local correlations scaled by local brightness and contrast comparisons, was introduced by Wang et al. [2004]. This correlationbased SSIM outperforms MSE in the similarity assessment of natural images. However, as correlation only measures linear dependence, distortions from multiple sources or nonlinear image processing such as nonlinear filtering can cause SSIM to under or over estimate the true structure similarity. In this article, we propose a new similarity measure that replaces the correlation and contrast comparisons of SSIM by a term obtained from a nonparametric test that has superior power to capture general dependence, including linear and nonlinear dependence in the conditional mean regression function as a special case. The new similarity measure applied to images from noise contamination, filtering, and watermarking, provides a more consistent image structure fidelity measure than commonly used measures. AMS 2000 subject classifications: Primary 68U10, 97K80, 62H35; secondary 62G10.