The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Computing geodesic paths on manifolds
Open accessAbstract
The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O ( M log M ) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Sethian, J. A. (1999) · Cited by 3,622
Self-citation
Cited by
Geodesic Convolutional Neural Networks on Riemannian Manifolds
Masci, J., Boscaini, D., Bronstein, M. M., & Vandergheynst, P. (2015) · 2015 IEEE International Conference on Computer Vision Workshop (ICCVW) · doi:10.1109/iccvw.2015.112 · Cited by 721
Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching
Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0508601103 · Cited by 538
Self-citationRobust single-view geometry and motion reconstruction
Li, H., Adams, B., Guibas, L. J., & Pauly, M. (2009) · ACM Transactions on Graphics · doi:10.1145/1618452.1618521 · Cited by 334
Bronstein, A. M., Bronstein, M. M., Kimmel, R., Mahmoudi, M., & Sapiro, G. (2010) · International Journal of Computer Vision · doi:10.1007/s11263-009-0301-6 · Cited by 267
Self-citationGeometric modeling in shape space
Kilian, M., Mitra, N. J., & Pottmann, H. (2007) · ACM SIGGRAPH 2007 papers · doi:10.1145/1275808.1276457 · Cited by 224
Metadata
- Authors
- Kimmel, R., & Sethian, J. A.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 1998-07-21
- Volume
- 95
- Issue
- 15
- Pages
- 8431-8435
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W1999690352
- Cited by
- 1,049
- References
- 1
- FWCI
- 9.56
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Computing geodesic paths on manifolds. https://app.cochat.ai/papers/10.1073/pnas.95.15.8431
- The paper
- Kimmel, R., & Sethian, J. A. (1998). Computing geodesic paths on manifolds. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.95.15.8431
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
