Measuring Objective Image and Video Quality: On the Relationship Between SSIM and PSNR for DCT-Based Compressed Images

Measuring accurately image and video quality is a critical step in any image and video processing and compression method and streaming/broadcasting system. In particular, simple and tractable objective metrics are required for quality-driven system optimization. This article aims to show how the structural similarity index (SSIM) for image quality assessment can be seen in many cases, such as discrete cosine transform (DCT)-based compressed images and video, as a content-aware version of the peak signal-to-noise ratio (PSNR) and it can be accurately estimated based on it. In fact, under some assumptions described in the article, the first can be derived directly from the latter based on a single content-dependent parameter, that is, the variance of the image/video frame. Tests on example images compressed via the Joint Photographic Expert Group (JPEG) at different quality levels further validate the assumptions and show how the proposed derivation can be utilized in replacement of the original expression of the SSIM for compressed images/video frames at quality levels of interest in real applications (e.g., video streaming). The robustness of the approximation is shown in the case of H.264 video compression. Finally, as an example application of the derivation, an expression is derived for measuring the image/video quality as a consequence of the image/video transcoding based on the SSIM.