The DOI matches its Crossref record; 49 of the 49 references it cites were found in a registry or an index.
Möbius voting for surface correspondence
Abstract
The goal of our work is to develop an efficient, automatic algorithm for discovering point correspondences between surfaces that are approximately and/or partially isometric. Our approach is based on three observations. First, isometries are a subset of the Möbius group, which has low-dimensionality -- six degrees of freedom for topological spheres, and three for topological discs. Second, computing the Möbius transformation that interpolates any three points can be computed in closed-form after a mid-edge flattening to the complex plane. Third, deviations from isometry can be modeled by a transportation-type distance between corresponding points in that plane. Motivated by these observations, we have developed a Möbius Voting algorithm that iteratively: 1) samples a triplet of three random points from each of two point sets, 2) uses the Möbius transformations defined by those triplets to map both point sets into a canonical coordinate frame on the complex plane, and 3) produces "votes" for predicted correspondences between the mutually closest points with magnitude representing their estimated deviation from isometry. The result of this process is a fuzzy correspondence matrix, which is converted to a permutation matrix with simple matrix operations and output as a discrete set of point correspondences with confidence values. The main advantage of this algorithm is that it can find intrinsic point correspondences in cases of extreme deformation. During experiments with a variety of data sets, we find that it is able to find dozens of point correspondences between different object types in different poses fully automatically.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Recent intrinsic techniques [36], [38], [39] use low dimensional embedding to by-pass the high-dimensionality problem by assuming a strong inelastic isometry constraint.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [39]
In the citing paper
“These transformations are similar to the domain theory in analytical learning-a global rule, one reason why these techniques can be cast as optimization problems and solved using the Hough transform [17], [39] or RANSAC technique [4], [71] efficiently.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [39]
Citations
Cites
Distinctive Image Features from Scale-Invariant Keypoints
Lowe, D. G. (2004) · International Journal of Computer Vision · doi:10.1023/b:visi.0000029664.99615.94 · Cited by 55,589
A Method for Registration of 3-D Shapes
Besl, P., & Mckay, N. D. (1992) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.121791 · Cited by 22,163
The Earth Mover's Distance as a Metric for Image Retrieval
Rubner, Y., Tomasi, C., & Guibas, L. (2000) · International Journal of Computer Vision · doi:10.1023/a:1026543900054 · Cited by 5,547
Generalizing the Hough transform to detect arbitrary shapes
Ballard, D. H. (1981) · Pattern Recognition · doi:10.1016/0031-3203(81)90009-1 · Cited by 4,434
Efficient variants of the ICP algorithm
Rusinkiewicz, S., & Levoy, M. (2002) · Proceedings Third International Conference on 3-D Digital Imaging and Modeling · doi:10.1109/im.2001.924423 · Cited by 3,945
Using spin images for efficient object recognition in cluttered 3D scenes
Johnson, A., & Hebert, M. (1999) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.765655 · Cited by 2,656
Discrete Differential-Geometry Operators for Triangulated 2-Manifolds
Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003) · Mathematics and visualization · doi:10.1007/978-3-662-05105-4_2 · Cited by 1,910
A new point matching algorithm for non-rigid registration
Chui, H., & Rangarajan, A. (2003) · Computer Vision and Image Understanding · doi:10.1016/s1077-3142(03)00009-2 · Cited by 1,560
SCAPE: shape completion and animation of people
Anguelov, D., Srinivasan, P., Koller, D., Thrun, S., Rodgers, J., & Davis, J. (2005) · ACM Transactions on Graphics · doi:10.1145/1073204.1073207 · Cited by 1,489
Computing Discrete Minimal Surfaces and Their Conjugates
Pinkall, U., & Polthier, K. (1993) · Experimental Mathematics · doi:10.1080/10586458.1993.10504266 · Cited by 1,278
Research works printed but not linked: 1
- 10.5555/1731309.1731327 · DOI
Cited by
Sorted by citations
Image Matching from Handcrafted to Deep Features: A Survey
Ma, J.-Y., Jiang, X., Fan, A., Jiang, J., & Yan, J. (2020) · International Journal of Computer Vision · doi:10.1007/s11263-020-01359-2 · Cited by 977
Bronstein, A. M., Bronstein, M. M., Guibas, L. J., & Ovsjanikov, M. (2011) · ACM Transactions on Graphics · doi:10.1145/1899404.1899405 · Cited by 811
The wave kernel signature: A quantum mechanical approach to shape analysis
Aubry, M., Schlickewei, U., & Cremers, D. (2011) · IEEE International Conference on Computer Vision Workshops · doi:10.1109/iccvw.2011.6130444 · Cited by 747
Ovsjanikov, M., Ben‐Chen, M., Solomon, J., Butscher, A., & Guibas, L. J. (2012) · ACM Transactions on Graphics · doi:10.1145/2185520.2185526 · Cited by 736
Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid
Tam, G. K. L., Cheng, Z.-Q., Lai, Y.-K., Langbein, F. C., Liu, Y., Marshall, D., Martin, R. R., Sun, X.-F., & Rosin, P. L. (2013) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2012.310 · Cited by 679
Metadata
- Authors
- Lipman, Y., & Funkhouser, T.
- Affiliations
- Princeton University (US)
- Venue
- ACM Transactions on Graphics
- Published
- 2009-07-27
- Volume
- 28
- Issue
- 3
- Pages
- 1-12
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W2105106232
- Cited by
- 332
- References
- 49
- Citations by year
- 2026: 6 · 2025: 7 · 2024: 4 · 2023: 8 · 2022: 15 · 2021: 3 · 2020: 15 · 2019: 13 · 2018: 27 · 2017: 25 · 2016: 34 · 2015: 18 · 2014: 37 · 2013: 38 · 2012: 30
- FWCI
- 27.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- ACM Transactions on Graphics (publishedVersion)
- Funders
- Division of Information and Intelligent Systems (CNFS-0406415IIS-0612231CCF-0702672)
- National Science Foundation (CNFS-0406415IIS-0612231CCF-0702672)
- Division of Computing and Communication Foundations (CNFS-0406415IIS-0612231CCF-0702672)
- Topics
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image Processing and 3D Reconstruction
- Keywords
- point matching, surface matching, Möbius transformations, isometries, transport distance, partial isometries
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
