The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
Blended intrinsic maps
Abstract
This paper describes a fully automatic pipeline for finding an intrinsic map between two non-isometric, genus zero surfaces. Our approach is based on the observation that efficient methods exist to search for nearly isometric maps (e.g., Möbius Voting or Heat Kernel Maps), but no single solution found with these methods provides low-distortion everywhere for pairs of surfaces differing by large deformations. To address this problem, we suggest using a weighted combination of these maps to produce a "blended map." This approach enables algorithms that leverage efficient search procedures, yet can provide the flexibility to handle large deformations. The main challenges of this approach lie in finding a set of candidate maps { m i } and their associated blending weights { b i ( p )} for every point p on the surface. We address these challenges specifically for conformal maps by making the following contributions. First, we provide a way to blend maps, defining the image of p as the weighted geodesic centroid of m i ( p ). Second, we provide a definition for smooth blending weights at every point p that are proportional to the area preservation of m i at p . Third, we solve a global optimization problem that selects candidate maps based both on their area preservation and consistency with other selected maps. During experiments with these methods, we find that our algorithm produces blended maps that align semantic features better than alternative approaches over a variety of data sets.
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In the citing paper
“[8], [9] that can handle near-to approximateisometric deformation.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
In the citing paper
“[8] uses sum of isometric distortion-difference of geodesic distances between the end-points of one correspondence with respect to all the other correspondences.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
In the citing paper
“[8] also recruited a volunteer to label 10-35 semantically meaningful and consistent feature points for each class of objects in the watertight meshes dataset [114].”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
In the citing paper
“For non-rigid shapes, many deformations are only near/approximateisometric, which may lead to matching ambiguities [8].”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
In the citing paper
“[8] has started in this direction using blended conformal maps.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [8]
Citations
Cites
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
Computing Discrete Minimal Surfaces and Their Conjugates
Pinkall, U., & Polthier, K. (1993) · Experimental Mathematics · doi:10.1080/10586458.1993.10504266 · Cited by 1,278
The space of human body shapes: reconstruction and parameterization from range scans
Allen, B., Curless, B., & Popović, Z. (2003) · ACM SIGGRAPH 2003 Papers · doi:10.1145/1201775.882311 · Cited by 913
Numerical Geometry of Non-Rigid Shapes
Bronstein, A. M., Bronstein, M. M., & Kimmel, R. (2008) · Texts and monographs in computer science · doi:10.1007/978-0-387-73301-2 · Cited by 767
The space of human body shapes
Allen, B., Curless, B., & Popović, Z. (2003) · ACM Transactions on Graphics · doi:10.1145/882262.882311 · Cited by 725
A Survey on Shape Correspondence
van Kaick, O. M., Zhang, H., Hamarneh, G., & Cohen‐Or, D. (2011) · Computer Graphics Forum · doi:10.1111/j.1467-8659.2011.01884.x · Cited by 606
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 555
Gelfand, N., Mitra, N. J., Guibas, L., & Pottmann, H. (2005) · doi:10.2312/sgp/sgp05/197-206 · Cited by 545
Möbius voting for surface correspondence
Lipman, Y., & Funkhouser, T. (2009) · ACM Transactions on Graphics · doi:10.1145/1531326.1531378 · Cited by 332
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Geometric Deep Learning: Going beyond Euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017) · IEEE Signal Processing Magazine · doi:10.1109/msp.2017.2693418 · Cited by 3,661
Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs
Monti, F., Boscaini, D., Masci, J., Rodola, E., Svoboda, J., & Bronstein, M. M. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.576 · Cited by 1,820
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
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
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
- Kim, V. G., Lipman, Y., & Funkhouser, T.
- Affiliations
- Princeton University (US)
- ORCID
- Kim, Vladimir G.
- Venue
- ACM Transactions on Graphics
- Published
- 2011-07
- Volume
- 30
- Issue
- 4
- Pages
- 1-12
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W4241422529
- Cited by
- 298
- References
- 27
- Citations by year
- 2026: 13 · 2025: 16 · 2024: 19 · 2023: 16 · 2022: 22 · 2021: 10 · 2020: 21 · 2019: 27 · 2018: 38 · 2017: 27 · 2016: 29 · 2015: 14 · 2014: 16 · 2013: 17 · 2012: 12
- FWCI
- 14.81
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- ACM Transactions on Graphics (publishedVersion)
- Funders
- Air Force Office of Scientific Research (1096101)
- Division of Computer and Network Systems (IIS-0612231CNS-0831374CCF-0702672CCF-0937139)
- Division of Computing and Communication Foundations (IIS-0612231CNS-0831374CCF-0702672CCF-0937139)
- Division of Information and Intelligent Systems (IIS-0612231CNS-0831374CCF-0702672CCF-0937139)
- 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 Graphics and Computer-Aided Design › Computational Geometry and Mesh Generation
- Keywords
- surface registration, genus zero surfaces, conformal mapping, area preservation, global optimization
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