# DeepWSD: Projecting Degradations in Perceptual Space to Wasserstein Distance in Deep Feature Space

arXiv: https://arxiv.org/abs/2208.03323 · HTML: https://mlsanity.com/paper/2208.03323/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 5 Aug 2022.

## Builds on (most cited first, 15 of 15)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Gradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index](https://mlsanity.com/paper/1308.3052/) (2013)
- [PieAPP: Perceptual Image-Error Assessment through Pairwise Preference](https://mlsanity.com/paper/1806.02067/) (2018)
- [Wasserstein Contrastive Representation Distillation](https://mlsanity.com/paper/2012.08674/) (2020)
- [Locally Adaptive Structure and Texture Similarity for Image Quality Assessment](https://mlsanity.com/paper/2110.08521/) (2021)
- [Projected Distribution Loss for Image Enhancement](https://mlsanity.com/paper/2012.09289/) (2020)
- [Quantifying Visual Image Quality: A Bayesian View](https://mlsanity.com/paper/2102.00195/) (2021)
- [No-Reference Image Quality Assessment by Hallucinating Pristine Features](https://mlsanity.com/paper/2108.04165/) (2021)
- [Comparison of Image Quality Models for Optimization of Image Processing Systems](https://mlsanity.com/paper/2005.01338/) (2020)
- [A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation](https://mlsanity.com/paper/2103.14799/) (2021)
- [Monge's Optimal Transport Distance for Image Classification](https://mlsanity.com/paper/1612.00181/) (2016)

## Built on by (most cited first, 20 of 20)

- [Exploring the Naturalness of AI-Generated Images](https://mlsanity.com/paper/2312.05476/) (2023)
- [Video Quality Assessment: A Comprehensive Survey](https://mlsanity.com/paper/2412.04508/) (2024)
- [Perceptual Quality Assessment of Face Video Compression: A Benchmark and An Effective Method](https://mlsanity.com/paper/2304.07056/) (2023)
- [Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measures](https://mlsanity.com/paper/2407.10181/) (2024)
- [DeepDC: Deep Distance Correlation as a Perceptual Image Quality Evaluator](https://mlsanity.com/paper/2211.04927/) (2022)
- [Deep Shape-Texture Statistics for Completely Blind Image Quality Evaluation](https://mlsanity.com/paper/2401.08107/) (2024)
- [Image Quality Assessment: Investigating Causal Perceptual Effects with Abductive Counterfactual Inference](https://mlsanity.com/paper/2412.16939/) (2024)
- [MILO: A Lightweight Perceptual Quality Metric for Image and Latent-Space Optimization](https://mlsanity.com/paper/2509.01411/) (2025)
- [Enhancing image quality prediction with self-supervised visual masking](https://mlsanity.com/paper/2305.19858/) (2023)
- [AgenticIQA: An Agentic Framework for Adaptive and Interpretable Image Quality Assessment](https://mlsanity.com/paper/2509.26006/) (2025)
- [From Global to Granular: Revealing IQA Model Performance via Correlation Surface](https://mlsanity.com/paper/2601.21738/) (2026)
- [Joint Quality Assessment and Example-Guided Image Processing by Disentangling Picture Appearance from Content](https://mlsanity.com/paper/2404.13484/) (2024)
- [Sliced Maximal Information Coefficient: A Training-Free Approach for Image Quality Assessment Enhancement](https://mlsanity.com/paper/2408.09920/) (2024)
- [Image Quality Assessment: Enhancing Perceptual Exploration and Interpretation with Collaborative Feature Refinement and Hausdorff distance](https://mlsanity.com/paper/2412.15847/) (2024)
- [VQualA 2025 Challenge on Visual Quality Comparison for Large Multimodal Models: Methods and Results](https://mlsanity.com/paper/2509.09190/) (2025)
- [Structured Uncertainty Similarity Score (SUSS): Learning a Probabilistic, Interpretable, Perceptual Metric Between Images](https://mlsanity.com/paper/2512.03701/) (2025)
- [Iterative Inference-time Scaling with Adaptive Frequency Steering for Image Super-Resolution](https://mlsanity.com/paper/2512.23532/) (2025)
- [Image Quality Assessment: Exploring Quality Awareness via Memory-driven Distortion Patterns Matching](https://mlsanity.com/paper/2602.18000/) (2026)
- [Causal Disentanglement-Inspired Degradation Representation Learning for Full-Reference Image Quality Assessment](https://mlsanity.com/paper/2604.21654/) (2026)
- [JLD: Perceptual Distance Through A Jacobian Lens](https://mlsanity.com/paper/2610.05967/) (2026)

## Abstract (arXiv)

Existing deep learning-based full-reference IQA (FR-IQA) models usually predict the image quality in a deterministic way by explicitly comparing the features, gauging how severely distorted an image is by how far the corresponding feature lies from the space of the reference images. Herein, we look at this problem from a different viewpoint and propose to model the quality degradation in perceptual space from a statistical distribution perspective. As such, the quality is measured based upon the Wasserstein distance in the deep feature domain. More specifically, the 1DWasserstein distance at each stage of the pre-trained VGG network is measured, based on which the final quality score is performed. The deep Wasserstein distance (DeepWSD) performed on features from neural networks enjoys better interpretability of the quality contamination caused by various types of distortions and presents an advanced quality prediction capability. Extensive experiments and theoretical analysis show the superiority of the proposed DeepWSD in terms of both quality prediction and optimization.