# Norm-in-Norm Loss with Faster Convergence and Better Performance for Image Quality Assessment

arXiv: https://arxiv.org/abs/2008.03889 · HTML: https://mlsanity.com/paper/2008.03889/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 30 of 54)

- [Exploring Video Quality Assessment on User Generated Contents from Aesthetic and Technical Perspectives](https://mlsanity.com/paper/2211.04894/) (2022)
- [Blind Image Quality Assessment via Vision-Language Correspondence: A Multitask Learning Perspective](https://mlsanity.com/paper/2303.14968/) (2023)
- [Towards A Better Metric for Text-to-Video Generation](https://mlsanity.com/paper/2401.07781/) (2024)
- [Neighbourhood Representative Sampling for Efficient End-to-end Video Quality Assessment](https://mlsanity.com/paper/2210.05357/) (2022)
- [DisCoVQA: Temporal Distortion-Content Transformers for Video Quality Assessment](https://mlsanity.com/paper/2206.09853/) (2022)
- [NTIRE 2022 Challenge on Perceptual Image Quality Assessment](https://mlsanity.com/paper/2206.11695/) (2022)
- [Continual Learning for Blind Image Quality Assessment](https://mlsanity.com/paper/2102.09717/) (2021)
- [Video compression dataset and benchmark of learning-based video-quality metrics](https://mlsanity.com/paper/2211.12109/) (2022)
- [Exploring the Naturalness of AI-Generated Images](https://mlsanity.com/paper/2312.05476/) (2023)
- [Universal Perturbation Attack on Differentiable No-Reference Image- and Video-Quality Metrics](https://mlsanity.com/paper/2211.00366/) (2022)
- [No-Reference Image Quality Assessment by Hallucinating Pristine Features](https://mlsanity.com/paper/2108.04165/) (2021)
- [UHD-IQA Benchmark Database: Pushing the Boundaries of Blind Photo Quality Assessment](https://mlsanity.com/paper/2406.17472/) (2024)
- [Quality-aware Pre-trained Models for Blind Image Quality Assessment](https://mlsanity.com/paper/2303.00521/) (2023)
- [Content-Variant Reference Image Quality Assessment via Knowledge Distillation](https://mlsanity.com/paper/2202.13123/) (2022)
- [Comparing the Robustness of Modern No-Reference Image- and Video-Quality Metrics to Adversarial Attacks](https://mlsanity.com/paper/2310.06958/) (2023)
- [SEAGULL: No-reference Image Quality Assessment for Regions of Interest via Vision-Language Instruction Tuning](https://mlsanity.com/paper/2411.10161/) (2024)
- [Bringing Textual Prompt to AI-Generated Image Quality Assessment](https://mlsanity.com/paper/2403.18714/) (2024)
- [KVQ: Boosting Video Quality Assessment via Saliency-guided Local Perception](https://mlsanity.com/paper/2503.10259/) (2025)
- [TractoSCR: A Novel Supervised Contrastive Regression Framework for Prediction of Neurocognitive Measures Using Multi-Site Harmonized Diffusion MRI Tractography](https://mlsanity.com/paper/2210.07411/) (2022)
- [KonX: Cross-Resolution Image Quality Assessment](https://mlsanity.com/paper/2212.05813/) (2022)
- [Gap-closing Matters: Perceptual Quality Evaluation and Optimization of Low-Light Image Enhancement](https://mlsanity.com/paper/2302.11464/) (2023)
- [Fast Adversarial CNN-based Perturbation Attack on No-Reference Image- and Video-Quality Metrics](https://mlsanity.com/paper/2305.15544/) (2023)
- [Defense Against Adversarial Attacks on No-Reference Image Quality Models with Gradient Norm Regularization](https://mlsanity.com/paper/2403.11397/) (2024)
- [AIM 2024 Challenge on Compressed Video Quality Assessment: Methods and Results](https://mlsanity.com/paper/2408.11982/) (2024)
- [Degraded Reference Image Quality Assessment](https://mlsanity.com/paper/2110.14899/) (2021)
- [Image Quality Assessment: Integrating Model-Centric and Data-Centric Approaches](https://mlsanity.com/paper/2207.14769/) (2022)
- [GMC-IQA: Exploiting Global-correlation and Mean-opinion Consistency for No-reference Image Quality Assessment](https://mlsanity.com/paper/2401.10511/) (2024)
- [High Resolution Image Quality Database](https://mlsanity.com/paper/2401.16087/) (2024)
- [Adversarial purification for no-reference image-quality metrics: applicability study and new methods](https://mlsanity.com/paper/2404.06957/) (2024)
- [Guardians of Image Quality: Benchmarking Defenses Against Adversarial Attacks on Image Quality Metrics](https://mlsanity.com/paper/2408.01541/) (2024)

## Abstract (arXiv)

Currently, most image quality assessment (IQA) models are supervised by the MAE or MSE loss with empirically slow convergence. It is well-known that normalization can facilitate fast convergence. Therefore, we explore normalization in the design of loss functions for IQA. Specifically, we first normalize the predicted quality scores and the corresponding subjective quality scores. Then, the loss is defined based on the norm of the differences between these normalized values. The resulting "Norm-in-Norm'' loss encourages the IQA model to make linear predictions with respect to subjective quality scores. After training, the least squares regression is applied to determine the linear mapping from the predicted quality to the subjective quality. It is shown that the new loss is closely connected with two common IQA performance criteria (PLCC and RMSE). Through theoretical analysis, it is proved that the embedded normalization makes the gradients of the loss function more stable and more predictable, which is conducive to the faster convergence of the IQA model. Furthermore, to experimentally verify the effectiveness of the proposed loss, it is applied to solve a challenging problem: quality assessment of in-the-wild images. Experiments on two relevant datasets (KonIQ-10k and CLIVE) show that, compared to MAE or MSE loss, the new loss enables the IQA model to converge about 10 times faster and the final model achieves better performance. The proposed model also achieves state-of-the-art prediction performance on this challenging problem. For reproducible scientific research, our code is publicly available at https://github.com/lidq92/LinearityIQA.