Estimating SSIM from MSE for DCT-Based Compressed Images
Authors: Luc Trudeau, Maria G. Martini
Organizations: Universit´e du Qu´ebec `a Rimouski, Rimouski, QC, Canada · Kingston University London, London, UK
Abstract
Efficient and perceptually meaningful quality assessment is a fundamental requirement for image and video processing, compression, and streaming systems. This article shows that, in the context of Discrete Cosine Transform ( DCT)-based compressed images, Structural Similarity Index ( SSIM ) can be approximated from global Peak Signal to Noise Ratio (PSNR) or Mean Square Error ( MSE) using local statistics derived only from the reference image. While prior work assumes access to local MSE, we propose two approaches to approximate local MSE by redistributing the global MSE using variance or standard-deviation-based weighting. Experiments on the Kodak and Xiph Subset1 datasets across a range of JPEG quality levels demonstrate that both approaches provide accurate and robust SSIM approximations, substantially outperforming the global MSE baseline. The proposed framework is designed to extend naturally to video, where reference-derived statistics can be amortized across multiple encodes of the same content.
Deep-feature-based perceptual similarity models have demonstrated strong alignment with human visual perception in Image Quality Assessment (IQA). However, most existing approaches operate at a single spatial scale, implicitly assuming that structural similarity at a fixed resolution is sufficient. The role of spatial scale in deep-feature similarity modeling thus remains insufficiently understood. In this letter, we isolate spatial scale as an independent factor using a minimal multiscale extension of DeepSSIM, referred to as Deep Structural Similarity with Multiscale Representation (MSDS). The proposed framework decouples deep feature representation from cross-scale integration by computing DeepSSIM independently across pyramid levels and fusing the resulting scores with a lightweight set of learnable global weights. Experiments on multiple benchmark datasets demonstrate consistent and statistically significant improvements over the single-scale baseline, while introducing negligible additional complexity. The results empirically confirm spatial scale as a non-negligible factor in deep perceptual similarity, isolated here via a minimal testbed.
Assessing the quality of single image super-resolution (SISR) results remains an open methodological problem. Common full-reference metrics (PSNR, SSIM, LPIPS) do not explicitly evaluate the preservation of the geometric structure of images, which is critical for the correctness of scale-based reconstruction. In addition, they require the forced alignment of images to the same size (\textit{forced resizing}), which introduces an external interpolation error into the evaluation process. This paper proposes a diagnostic scale-invariant quality measure, MSIQ (\textit{Moment-based Scale-Invariant Quality}), based on the comparison of normalized central geometric moments of two images. MSIQ enables direct comparison of images with different spatial resolutions without resizing, is mathematically deterministic (\textit{model-free}), and has an analytical form. To provide a theoretical basis for the approach, we introduce a conceptual distinction between the ability of metrics to monotonically track degradation (\textit{tracking ability}) and their geometric selectivity (\textit{geometric specificity}). The experimental validation confirmed the stability of MSIQ under uniform scaling and, at the same time, revealed the high sensitivity of traditional metrics to the choice of interpolation method. The results show that MSIQ has pronounced geometric selectivity: the proposed measure effectively separates geometric deformations from non-geometric artifacts, in particular JPEG compression, unlike pixel-based and perceptual metrics. It is also shown that the response of MSIQ to structural perturbations remains stable across different classes of SR algorithms, including DNN models with different architectures. The proposed measure is a complementary diagnostic tool for domains where geometric fidelity has priority, in particular medical imaging and remote sensing.
Recent advances in conventional and learning-based image coding have increased the demand for benchmark datasets that support fine-grained assessment of compressed image quality, particularly for learning-based image compression methods. This paper introduces Assessment of Image Coding 2026 (AIC2026), a large-scale dataset for high-fidelity image compression containing 70 source images selected from 2,787 candidates using semantic clustering, inter-metric disagreement among objective image quality assessment (IQA) methods, and manual inspection and refinement. The dataset covers a wide range of compression artifacts produced by eight conventional and four learning-based codecs across 17 coding configurations. Each source image is encoded using seven codecs. For each source-codec pair, decoded images are provided at 20 perceptually spaced distortion levels, corresponding approximately to 0.2-4.0 just-noticeable difference (JND) units using the ColorVideoVDP (CVVDP) metric for distortion estimation, yielding 9,618 distorted images. This fine-grained sampling enables analysis of rate-distortion behavior and objective metric evaluation for subtle quality differences across a wide range of compression artifacts. We report an extensive objective analysis using 24 conventional and 12 learning-based IQA methods. The results show substantial disagreement among current IQA methods for fine-grained quality differences, particularly for artifacts introduced by learning-based codecs. The complete dataset is publicly available at https://doi.org/10.18419/DARUS-6156.