# MSIQ: Moment-based Scale-Invariant Quality Measure for Single Image Super-Resolution

arXiv: https://arxiv.org/abs/2605.17588 · HTML: https://mlsanity.com/paper/2605.17588/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 52 references that are in the map.
- First posted on arXiv 17 May 2026.

## Builds on (most cited first, 22 of 22)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [SeeSR: Towards Semantics-Aware Real-World Image Super-Resolution](https://mlsanity.com/paper/2311.16518/) (2023)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [Learning a No-Reference Quality Metric for Single-Image Super-Resolution](https://mlsanity.com/paper/1612.05890/) (2016)
- [Real-World Single Image Super-Resolution: A Brief Review](https://mlsanity.com/paper/2103.02368/) (2021)
- [A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment](https://mlsanity.com/paper/1607.06140/) (2016)
- [Mean Deviation Similarity Index: Efficient and Reliable Full-Reference Image Quality Evaluator](https://mlsanity.com/paper/1608.07433/) (2016)
- [Quality Assessment of Image Super-Resolution: Balancing Deterministic and Statistical Fidelity](https://mlsanity.com/paper/2207.08689/) (2022)
- [Augmenting Perceptual Super-Resolution via Image Quality Predictors](https://mlsanity.com/paper/2504.18524/) (2025)
- [Efficient Deep Neural Network for Photo-realistic Image Super-Resolution](https://mlsanity.com/paper/1903.02240/) (2019)
- [Towards True Detail Restoration for Super-Resolution: A Benchmark and a Quality Metric](https://mlsanity.com/paper/2203.08923/) (2022)
- [2D moment invariants from the point of view of the classical invariant theory](https://mlsanity.com/paper/1908.08927/) (2019)
- [Self-Supervised Image Super-Resolution Quality Assessment based on Content-Free Multi-Model Oriented Representation Learning](https://mlsanity.com/paper/2602.10744/) (2026)

## Abstract (arXiv)

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 (textitforced resizing), which introduces an external interpolation error into the evaluation process. This paper proposes a diagnostic scale-invariant quality measure, MSIQ (textitMoment-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 (textitmodel-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 (textittracking ability) and their geometric selectivity (textitgeometric 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.