Einstein Relativity Transform (ERT) method for image compression: Relating the behavior of the transform to the intensity histogram of grayscale images via segmentation

Abstract

This paper aims to improve the performance of the recently proposed image compression method called Einstein Relativity Transform (ERT) by (i) slightly modifying the ERT equation and (ii) understanding its behavior by performing parameter segmentation. This is done in three steps. First, we calculated the histograms of three different images as our sampled input images. Second, we measured their quality performances according to their (1) peak signal-to-noise ratio (PSNR), (2) structural similarity index measure (SSIM), and (3) compression ratio (CR) using quantization method (QM) via percent max using 5%, 10%, 15%, and 20% criteria proposed by Narag and Dingel [Proc. SPP, SPP-2023-PB-05]. We then divided the operational p values into six segments (A, B, C, D, E, and F) based on the observed behavior of p. Finally, we related these segments to the histogram of the images. We observed that the trends present in the plots are consistent across all three images despite the presence of many subsequent spikes and dips. This implies that parameter p has an internal "logic" and that determining the best value of p is reliant on parameters within the images themselves.