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Coupled Optimal Transport with Landmark Constraints — arXiv:2608.19783

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.19783
License (as archived): CC0-1.0
Archived: 2026-10-18T12:04:40.383Z
SHA-256 of the archived text: 46981157fea037fae42f5859fc0b51f34fd806d4fec08b1855ec33685ec572ee
Stable URL of this page: https://metraipolis.com/documento/dc_dcff5d76eff8

How to cite

Coupled Optimal Transport with Landmark Constraints — arXiv:2608.19783 — arXiv (en), https://arxiv.org/abs/2608.19783 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dcff5d76eff8 (Metraipolis archive dc_dcff5d76eff8, sha256 46981157fea037fae42f5859fc0b51f34fd806d4fec08b1855ec33685ec572ee)

BibTeX

@misc{dcdcff5d76eff8,
  title = {Coupled Optimal Transport with Landmark Constraints — arXiv:2608.19783},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.19783},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dcff5d76eff8; sha256 46981157fea037fae42f5859fc0b51f34fd806d4fec08b1855ec33685ec572ee},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.19783. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion. However, minimizing transport cost or distortion alone may fail to identify a geometrically meaningful transformation between the two distributions. To address this limitation, this paper proposes a novel coupled OT framework that leverages a small number of annotated landmarks to guide the recovery of an underlying deformation governing the distribution transformation. The coupled OT framework integrates the optimization of the transport plan and the deformation field into a unified model, where the landmark-guided deformation field and the cost-driven transport plan are coupled through a mutual-consistency constraint. As a result, the deformation is jointly determined by the annotated landmarks and cost-driven distribution matching. The proposed framework provides a principled connection between landmark-based registration and transport-based distribution matching, enabling the recovery of transport maps from sparse geometric supervision. We establish the well-definedness of the proposed model in a general variational setting and develop a finite-element-based numerical algorithm for computation whose convergence properties are systematically analyzed. The practical effectiveness of the proposed approach is verified in shape matching.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-21 in cs.CV).
Categorie arXiv: Computer Vision and Pattern Recognition (cs.CV).
Pagina del lavoro: https://arxiv.org/abs/2608.19783 — 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 2026-10-18T12:01:57.716Z dalla pagina https://arxiv.org/catchup/cs.CV/2026-08-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).