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Quantifying the noise sensitivity of the Wasserstein metric for images — arXiv:2510.01015

Source: arXiv (en)
Original: https://arxiv.org/abs/2510.01015
License (as archived): CC0-1.0
Archived: 2026-10-19T06:19:36.362Z
SHA-256 of the archived text: ed6ae966e29ceb4962c7c18b28bc21eed6af57a9b78afd8c958fc2d98f9bcb9c
Stable URL of this page: https://metraipolis.com/documento/dc_d47bfefdbeea

How to cite

Quantifying the noise sensitivity of the Wasserstein metric for images — arXiv:2510.01015 — arXiv (en), https://arxiv.org/abs/2510.01015 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d47bfefdbeea (Metraipolis archive dc_d47bfefdbeea, sha256 ed6ae966e29ceb4962c7c18b28bc21eed6af57a9b78afd8c958fc2d98f9bcb9c)

BibTeX

@misc{dcd47bfefdbeea,
  title = {Quantifying the noise sensitivity of the Wasserstein metric for images — arXiv:2510.01015},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2510.01015},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d47bfefdbeea; sha256 ed6ae966e29ceb4962c7c18b28bc21eed6af57a9b78afd8c958fc2d98f9bcb9c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2510.01015. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Wasserstein metrics are increasingly adopted as similarity scores for images. We consider the sensitivity of Wasserstein metrics with respect to pixel-wise additive noise when the images are treated as discrete measures on the pixel grid. We derive finite-sample expectation bounds for a Gaussian noise model. Among other results, we prove that the error in the signed 2-Wasserstein discrepancy scales with the square root of the noise standard deviation. This is favorable compared to the Euclidean metric that scales linearly, and thus provides a theoretical basis for the benefits of optimal transport distances in noisy settings. We present experiments that support our theoretical findings and point to a peculiar phenomenon where increasing the level of noise can decrease the Wasserstein distance. A case study on cryo-electron microscopy images demonstrates that the Wasserstein metric can capture the geometry of the data manifold in high noise settings even when the Euclidean metric fails.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-12 in cs.LG).
Categorie arXiv: Statistics Theory (math.ST) ; Machine Learning (cs.LG); Image and Video Processing (eess.IV).
Pagina del lavoro: https://arxiv.org/abs/2510.01015 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T06:11:45.113Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-12?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).