# Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measures

arXiv: https://arxiv.org/abs/2407.10181 · HTML: https://mlsanity.com/paper/2407.10181/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 57 references that are in the map.
- First posted on arXiv 14 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [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)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [SinGAN: Learning a Generative Model from a Single Natural Image](https://mlsanity.com/paper/1905.01164/) (2019)
- [Style Transfer by Relaxed Optimal Transport and Self-Similarity](https://mlsanity.com/paper/1904.12785/) (2019)
- [PieAPP: Perceptual Image-Error Assessment through Pairwise Preference](https://mlsanity.com/paper/1806.02067/) (2018)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Shift-tolerant Perceptual Similarity Metric](https://mlsanity.com/paper/2207.13686/) (2022)
- [Locally Adaptive Structure and Texture Similarity for Image Quality Assessment](https://mlsanity.com/paper/2110.08521/) (2021)
- [An Unsupervised Information-Theoretic Perceptual Quality Metric](https://mlsanity.com/paper/2006.06752/) (2020)
- [Generating natural images with direct Patch Distributions Matching](https://mlsanity.com/paper/2203.11862/) (2022)
- [DeepWSD: Projecting Degradations in Perceptual Space to Wasserstein Distance in Deep Feature Space](https://mlsanity.com/paper/2208.03323/) (2022)
- [Learning Implicit Generative Models by Matching Perceptual Features](https://mlsanity.com/paper/1904.02762/) (2019)
- [Measuring Perceptual Color Differences of Smartphone Photographs](https://mlsanity.com/paper/2205.13489/) (2022)
- [Guetzli: Perceptually Guided JPEG Encoder](https://mlsanity.com/paper/1703.04421/) (2017)
- [Learning a Deep Color Difference Metric for Photographic Images](https://mlsanity.com/paper/2303.14964/) (2023)

## Built on by (most cited first, 14 of 14)

- [Free-Lunch Color-Texture Disentanglement for Stylized Image Generation](https://mlsanity.com/paper/2503.14275/) (2025)
- [HAODiff: Human-Aware One-Step Diffusion via Dual-Prompt Guidance](https://mlsanity.com/paper/2505.19742/) (2025)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Evaluating quality metrics through the lenses of psychophysical measurements of low-level vision](https://mlsanity.com/paper/2503.16264/) (2025)
- [HonestFace: Towards Honest Face Restoration with One-Step Diffusion Model](https://mlsanity.com/paper/2505.18469/) (2025)
- [Adversarial Concept Distillation for One-Step Diffusion Personalization](https://mlsanity.com/paper/2510.20512/) (2025)
- [Evaluating Low-Light Image Enhancement Across Multiple Intensity Levels](https://mlsanity.com/paper/2511.15496/) (2025)
- [DriftScope: Measuring The Hidden Effects of Diffusion Model Adaptation](https://mlsanity.com/paper/2607.00183/) (2026)
- [ReSWD: ReSTIR'd, not shaken. Combining Reservoir Sampling and Sliced Wasserstein Distance for Variance Reduction](https://mlsanity.com/paper/2510.01061/) (2025)
- [Light Up Your Face: A Physically Consistent Dataset and Diffusion Model for Face Fill-Light Enhancement](https://mlsanity.com/paper/2602.04300/) (2026)
- [Bricker to BRACE: A Bracket Exposure RAW Dataset and Restoration Model for Flicker-Banding](https://mlsanity.com/paper/2606.29845/) (2026)
- [StyleComposer: Training-Free Multi-Reference Style Composition](https://mlsanity.com/paper/2608.05213/) (2026)
- [Perceptual Color Difference Modeling Using Machine Learning and Human Similarity Judgments](https://mlsanity.com/paper/2609.39130/) (2026)
- [DiDE:Direct Injection with Color-Texture DEcoupling for 3D Stylization](https://mlsanity.com/paper/2610.02044/) (2026)

## Abstract (arXiv)

Contemporary color difference (CD) measures for photographic images typically operate by comparing co-located pixels, patches in a ``perceptually uniform'' color space, or features in a learned latent space. Consequently, these measures inadequately capture the human color perception of misaligned image pairs, which are prevalent in digital photography (e.g., the same scene captured by different smartphones). In this paper, we describe a perceptual CD measure based on the multiscale sliced Wasserstein distance, which facilitates efficient comparisons between non-local patches of similar color and structure. This aligns with the modern understanding of color perception, where color and structure are inextricably interdependent as a unitary process of perceptual organization. Meanwhile, our method is easy to implement and training-free. Experimental results indicate that our CD measure performs favorably in assessing CDs in photographic images, and consistently surpasses competing models in the presence of image misalignment. Additionally, we empirically verify that our measure functions as a metric in the mathematical sense, and show its promise as a loss function for image and video color transfer tasks. The code is available at https://github.com/real-hjq/MS-SWD.