Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measures | SpringerLink
Skip to main content
Springer Nature Link
Log in

Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measures

  • Conference paper
  • First Online:
Computer Vision – ECCV 2024 (ECCV 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15111))

Included in the following conference series:

  • 115 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 8465
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 10581
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Histogram intersection measures the similarity between two normalized histograms by summing the minimum values of corresponding bins.

  2. 2.

    This corresponds to solving a large-scale linear programming problem, which is painfully slow.

References

  1. Alakuijala, J., Obryk, R., Stoliarchuk, O., Szabadka, Z., Vandevenne, L., Wassenberg, J.: Guetzli: perceptually guided JPEG encoder. arXiv preprint arXiv:1703.04421 (2017)

  2. Albertazzi, L., Van Tonder, G.J., Vishwanath, D.: Perception Beyond Inference: The Information Content of Visual Processes. MIT Press, Cambridge (2011)

    Book  Google Scholar 

  3. Andersson, P., Nilsson, J., Akenine-Möller, T., Oskarsson, M., Åström, K., Fairchild, M.D.: FLIP: a difference evaluator for alternating images. ACM Comput. Graph. Interact. Techn. 3(2), 1–23 (2020)

    Google Scholar 

  4. Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein generative adversarial networks. In: International Conference on Machine Learning, pp. 214–223 (2017)

    Google Scholar 

  5. Barnes, C., Shechtman, E., Finkelstein, A., Goldman, D.B.: PatchMatch: a randomized correspondence algorithm for structural image editing. ACM Trans. Graph. 28(3), 1–11 (2009)

    Article  Google Scholar 

  6. Ben-Shahar, O., Zucker, S.W.: Hue geometry and horizontal connections. Neural Netw. 17(5–6), 753–771 (2004)

    Article  Google Scholar 

  7. Bhardwaj, S., Fischer, I., Ballé, J., Chinen, T.: An unsupervised information-theoretic perceptual quality metric. In: International Conference on Neural Information Processing Systems, pp. 1–12 (2020)

    Google Scholar 

  8. Burt, P.J., Adelson, E.H.: The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31(4), 532–540 (1983)

    Article  Google Scholar 

  9. Chen, H., Wang, Z., Yang, Y., Sun, Q., Ma, K.: Learning a deep color difference metric for photographic images. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 22242–22251 (2023)

    Google Scholar 

  10. Chou, C.H., Liu, K.C.: A fidelity metric for assessing visual quality of color images. In: International Conference on Computer Communications and Networks, pp. 1154–1159 (2007)

    Google Scholar 

  11. Choudhury, A., Wanat, R., Pytlarz, J., Daly, S.: Image quality evaluation for high dynamic range and wide color gamut applications using visual spatial processing of color differences. Color Res. Appl. 46(1), 46–64 (2021)

    Article  Google Scholar 

  12. Clarke, F.J.J., McDonald, R., Rigg, B.: Modification to the JPC79 colour-difference formula. J. Soc. Dyers Colour. 100(4), 128–132 (1984)

    Article  Google Scholar 

  13. Deshpande, I., Zhang, Z., Schwing, A.: Generative modeling using the sliced Wasserstein distance. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 3483–3491 (2018)

    Google Scholar 

  14. Ding, K., Liu, Y., Zou, X., Wang, S., Ma, K.: Locally adaptive structure and texture similarity for image quality assessment. In: ACM International Conference on Multimedia, pp. 2483–2491 (2021)

    Google Scholar 

  15. Ding, K., Ma, K., Wang, S., Simoncelli, E.P.: Comparison of full-reference image quality models for optimization of image processing systems. Int. J. Comput. Vision 129(4), 1258–1281 (2021)

    Article  Google Scholar 

  16. Ding, K., Ma, K., Wang, S., Simoncelli, E.P.: Image quality assessment: unifying structure and texture similarity. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2567–2581 (2022)

    Google Scholar 

  17. Elnekave, A., Weiss, Y.: Generating natural images with direct patch distributions matching. In: European Conference on Computer Vision, pp. 544–560. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-19790-1_33

  18. Fairchild, M.D.: Color Appearance Models. John Wiley & Sons, Ltd., Hoboken (2013)

    Book  Google Scholar 

  19. Garcia, P.A., Huertas, R., Melgosa, M., Cui, G.: Measurement of the relationship between perceived and computed color differences. J. Opt. Soc. Am. A 24(7), 1823–1829 (2007)

    Article  Google Scholar 

  20. Ghildyal, A., Liu, F.: Shift-tolerant perceptual similarity metric. In: European Conference on Computer Vision, pp. 91—107. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-19797-0_6

  21. Hong, G., Luo, M.R.: New algorithm for calculating perceived colour difference of images. Imaging Sci. J. 54(2), 86–91 (2006)

    Article  Google Scholar 

  22. Kanizsa, G.: Organization in Vision: Essays on Gestalt Perception. Praeger Publishers, Westport (1979)

    Google Scholar 

  23. Karras, T., Aila, T., Laine, S., Lehtinen, J.: Progressive growing of GANs for improved quality, stability, and variation. In: International Conference on Learning Representations, pp. 1–26 (2018)

    Google Scholar 

  24. Kolkin, N., Salavon, J., Shakhnarovich, G.: Style transfer by relaxed optimal transport and self-similarity. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 10051–10060 (2019)

    Google Scholar 

  25. Lee, S.M., Xin, J.H., Westland, S.: Evaluation of image similarity by histogram intersection. Color Res. Appl. 30(4), 265–274 (2005)

    Article  Google Scholar 

  26. Lennie, P.: Color coding in the cortex. In: Color Vision: From Genes to Perception, pp. 235–247 (1999)

    Google Scholar 

  27. Li, C., et al.: A revision of CIECAM02 and its CAT and UCS. In: Color and Imaging Conference, pp. 208–212 (2016)

    Google Scholar 

  28. Liao, X., Chen, B., Zhu, H., Wang, S., Zhou, M., Kwong, S.: DeepWSD: projecting degradations in perceptual space to Wasserstein distance in deep feature space. In: ACM International Conference on Multimedia, pp. 970–978 (2022)

    Google Scholar 

  29. Luo, M.R., Cui, G., Rigg, B.: The development of the CIE 2000 colour-difference formula: CIEDE2000. Color Res. Appl. 26(5), 340–350 (2001)

    Article  Google Scholar 

  30. Luo, M.R., Li, C.: CIECAM02 and its recent developments. In: Advanced Color Image Processing and Analysis, pp. 19–58 (2013)

    Google Scholar 

  31. Mahy, M., Van Eycken, L., Oosterlinck, A.: Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV. Color Res. Appl. 19(2), 105–121 (1994)

    Article  Google Scholar 

  32. McDonald, R., Smith, K.J.: CIE94-A new colour-difference formula. J. Soc. Dyers Colour. 111(12), 376–379 (1995)

    Article  Google Scholar 

  33. Moroney, N., Fairchild, M.D., Hunt, R.W., Li, C., Luo, M.R., Newman, T.: The CIECAM02 color appearance model. In: Color and Imaging Conference, pp. 23–27 (2002)

    Google Scholar 

  34. Ortiz-Jaramillo, B., Kumcu, A., Platisa, L., Philips, W.: Evaluation of color differences in natural scene color images. Signal Process. Image Commun. 71, 128–137 (2019)

    Article  Google Scholar 

  35. Ouni, S., Zagrouba, E., Chambah, M., Herbin, M.: A new spatial colour metric for perceptual comparison. In: International Conference on E-Systems Engineering, Communication and Information, pp. 413–428 (2008)

    Google Scholar 

  36. Pitie, F., Kokaram, A.C., Dahyot, R.: N-dimensional probability density function transfer and its application to color transfer. In: IEEE International Conference on Computer Vision, pp. 1434–1439 (2005)

    Google Scholar 

  37. Prashnani, E., Cai, H., Mostofi, Y., Sen, P.: PieAPP: perceptual image-error assessment through pairwise preference. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1808–1817 (2018)

    Google Scholar 

  38. Rabin, J., Peyré, G., Delon, J., Bernot, M.: Wasserstein barycenter and its application to texture mixing. In: International Conference on Scale Space and Variational Methods in Computer Vision, pp. 435–446 (2012)

    Google Scholar 

  39. Robertson, A.R.: The CIE 1976 color-difference formulae. Color Res. Appl. 2(1), 7–11 (1977)

    Article  Google Scholar 

  40. Santos, C.N.d., Mroueh, Y., Padhi, I., Dognin, P.: Learning implicit generative models by matching perceptual features. In: IEEE International Conference on Computer Vision, pp. 4461–4470 (2019)

    Google Scholar 

  41. Shaham, T.R., Dekel, T., Michaeli, T.: SinGAN: learning a generative model from a single natural image. In: IEEE International Conference on Computer Vision, pp. 4570–4580 (2019)

    Google Scholar 

  42. Shapley, R., Hawken, M.J.: Color in the cortex: single-and double-opponent cells. Vision. Res. 51(7), 701–717 (2011)

    Article  Google Scholar 

  43. Sharma, G., Bala, R.: Digital Color Imaging Handbook. CRC Press, Boca Raton (2017)

    Google Scholar 

  44. Shen, H.C., Wong, A.K.: Generalized texture representation and metric. Comput. Vision Graph. Image Process. 23(2), 187–206 (1983)

    Article  Google Scholar 

  45. Shevell, S.K., Kingdom, F.A.A.: Color in complex scenes. Ann. Rev. Psychol. 59, 143–166 (2008)

    Article  Google Scholar 

  46. Shocher, A., Bagon, S., Isola, P., Irani, M.: InGAN: capturing and retargeting the “DNA” of a natural image. In: IEEE International Conference on Computer Vision, pp. 4492–4501 (2019)

    Google Scholar 

  47. Simakov, D., Caspi, Y., Shechtman, E., Irani, M.: Summarizing visual data using bidirectional similarity. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2008)

    Google Scholar 

  48. Simoncelli, E.P., Freeman, W.T.: The steerable pyramid: a flexible architecture for multi-scale derivative computation. In: IEEE International Conference on Image Processing, pp. 444–447 (1995)

    Google Scholar 

  49. Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. In: International Conference on Learning Representations, pp. 1–14 (2015)

    Google Scholar 

  50. VQEG: Final report from the Video Quality Experts Group on the validation of objective models of video quality assessment (2000). http://www.vqeg.org

  51. Wang, Z., et al.: CD-iNet: deep invertible network for perceptual image color difference measurement. Int. J. Comput. Vision (2024)

    Google Scholar 

  52. Wang, Z., et al.: Measuring perceptual color differences of smartphone photography. IEEE Trans. Pattern Anal. Mach. Intell. 45(8), 10114–10128 (2023)

    Article  Google Scholar 

  53. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Article  Google Scholar 

  54. Wang, Z., Simoncelli, E.P., Bovik, A.C.: Multiscale structural similarity for image quality assessment. In: Asilomar Conference on Signals, Systems & Computers, pp. 1398–1402 (2003)

    Google Scholar 

  55. Xu, K., et al.: A database of visual color differences of modern smartphone photography. In: IEEE International Conference on Image Processing, pp. 3758–3762 (2022)

    Google Scholar 

  56. Zhang, R., Isola, P., Efros, A.A., Shechtman, E., Wang, O.: The unreasonable effectiveness of deep features as a perceptual metric. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 586–595 (2018)

    Google Scholar 

  57. Zhang, X., Wandell, B.A.: A spatial extension of CIELAB for digital color-image reproduction. J. Soc. Inf. Display 5(1), 61–63 (1997)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Key Research and Development Program of China (2023YFE0210700), the Hong Kong ITC Innovation and Technology Fund (9440390), the National Natural Science Foundation of China (62071407, 62375233, 62301323, 62441203, 62302423, and 62311530101), and the Shenzhen Natural Science Foundation (20231128191435002).

Author information

Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Hong Kong, China

    Jiaqi He & Kede Ma

  2. Shenzhen Research Institute, City University of Hong Kong, Hong Kong, China

    Jiaqi He & Kede Ma

  3. Department of Engineering, Shenzhen MSU-BIT University, Shenzhen, China

    Zhihua Wang

  4. Guangdong OPPO Mobile Telecommunications Corp., Ltd., Dongguan, China

    Leon Wang & Tsein-I Liu

  5. School of Information Management, Jiangxi University of Finance and Economics, Nanchang, China

    Yuming Fang

  6. School of Data Science, The Chinese University of Hong Kong (Shenzhen), Shenzhen, China

    Qilin Sun

Authors
  1. Jiaqi He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhihua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Leon Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Tsein-I Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuming Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Qilin Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Kede Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qilin Sun .

Editor information

Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Aleš Leonardis

  2. University of Trento, Trento, Italy

    Elisa Ricci

  3. Technical University of Darmstadt, Darmstadt, Germany

    Stefan Roth

  4. Princeton University, Princeton, NJ, USA

    Olga Russakovsky

  5. Czech Technical University in Prague, Prague, Czech Republic

    Torsten Sattler

  6. École des Ponts ParisTech, Marne-la-Vallée, France

    Gül Varol

Rights and permissions

Reprints and permissions

Copyright information

© 2025 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

He, J. et al. (2025). Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measures. In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G. (eds) Computer Vision – ECCV 2024. ECCV 2024. Lecture Notes in Computer Science, vol 15111. Springer, Cham. https://doi.org/10.1007/978-3-031-73668-1_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-73668-1_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-73667-4

  • Online ISBN: 978-3-031-73668-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation