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Direct Topology Tracking in Continuous Implicit Models — arXiv:2609.12157

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.12157
License (as archived): CC0-1.0
Archived: 2026-10-16T03:16:02.506Z
SHA-256 of the archived text: 2bbb96722160b8f4e66bafb4dfcb1788e2273b88479d142bbcfc63c8ed80a06e
Stable URL of this page: https://metraipolis.com/documento/dc_ca339348b3da

How to cite

Direct Topology Tracking in Continuous Implicit Models — arXiv:2609.12157 — arXiv (en), https://arxiv.org/abs/2609.12157 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ca339348b3da (Metraipolis archive dc_ca339348b3da, sha256 2bbb96722160b8f4e66bafb4dfcb1788e2273b88479d142bbcfc63c8ed80a06e)

BibTeX

@misc{dcca339348b3da,
  title = {Direct Topology Tracking in Continuous Implicit Models — arXiv:2609.12157},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.12157},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ca339348b3da; sha256 2bbb96722160b8f4e66bafb4dfcb1788e2273b88479d142bbcfc63c8ed80a06e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.12157. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We present a framework for tracking topological features directly within continuous implicit models. Such models, including implicit neural representations (INRs) and multivariate functional approximations (MFAs), are increasingly adopted to represent scientific data without the resolution constraints of discrete grids. They offer compact, smooth, and differentiable representations of complex fields, enabling new opportunities for high-performance data storage, reconstruction, and analysis. Given a continuous implicit model, our method tracks the evolution of critical points by querying the model and its derivatives, thereby eliminating the need to resample onto a grid. This approach enables faithful feature tracking while avoiding discretization-induced artifacts such as aliasing. We demonstrate the generality of our framework across a range of implicit representations, including analytic functions, MFAs, and INRs, and show that it produces smooth, coherent critical point trajectories. By enabling feature tracking directly on continuous representations, our method supports a new class of feature-driven visualization workflows centered on implicit models.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-14 in cs.LG).
Categorie arXiv: Computational Geometry (cs.CG) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.12157 — 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 2026-10-16T03:05:44.100Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).