A new class of wavelet-based metrics for image similarity assessment

In this paper, we propose a new class of image similarity metrics based on a wavelet decomposition. By suitably combining weighted contributions of the different dyadic frequency bands, we define a class of similarity measures and we prove it is a metric. Moreover, we discuss the theoretical relationship between the novel class of metrics and the well-known structural similarity index (SSIM) and its multiscale versions (MSSSIM and CWSSIM). By using standard benchmark indexes over a reference database in the literature (the TID2013 database), we test the efficiency of the newly defined metrics in performing similarity assessment. We compare the performance of our metric with other well-known indexes in the literature, such as SSIM, FPH, MSSSIM, CWSSIM and PSNR, to demonstrate its improvement over the current state of the art, which becomes more evident when the query image is the one identified by the worst level of degradation which is perceived by the human visual system, as coded by the standard mean opinion score stored in the database.