The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Spectral Geometry Processing with Manifold Harmonics
Open accessAbstract
We present an explicit method to compute a generalization of the Fourier Transform on a mesh. It is well known that the eigenfunctions of the Laplace Beltrami operator (Manifold Harmonics) define a function basis allowing for such a transform. However, computing even just a few eigenvectors is out of reach for meshes with more than a few thousand vertices, and storing these eigenvectors is prohibitive for large meshes. To overcome these limitations, we propose a band‐by‐band spectrum computation algorithm and an out‐of‐core implementation that can compute thousands of eigenvectors for meshes with up to a million vertices. We also propose a limited‐memory filtering algorithm, that does not need to store the eigenvectors. Using this latter algorithm, specific frequency bands can be filtered, without needing to compute the entire spectrum. Finally, we demonstrate some applications of our method to interactive convolution geometry filtering. These technical achievements are supported by a solid yet simple theoretic framework based on Discrete Exterior Calculus (DEC). In particular, the issues of symmetry and discretization of the operator are considered with great care.
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Cites
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 1,889
A signal processing approach to fair surface design
Taubin, G. (1995) · Proceedings of the 22nd annual conference on Computer graphics and interactive techniques - SIGGRAPH '95 · doi:10.1145/218380.218473 · Cited by 1,855
Computing Discrete Minimal Surfaces and Their Conjugates
Pinkall, U., & Polthier, K. (1993) · Experimental Mathematics · doi:10.1080/10586458.1993.10504266 · Cited by 1,249
Interactive multi-resolution modeling on arbitrary meshes
Kobbelt, L., Campagna, S., Vorsatz, J., & Seidel, H.-P. (1998) · Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98 · doi:10.1145/280814.280831 · Cited by 655
Spectral compression of mesh geometry
Karni, Z., & Gotsman, C. (2000) · Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00 · doi:10.1145/344779.344924 · Cited by 652
MAPS: multiresolution adaptive parameterization of surfaces
Lee, A. W. F., Sweldens, W., Schröder, P., Cowsar, L., & Dobkin, D. (1998) · Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98 · doi:10.1145/280814.280828 · Cited by 626
Multiresolution signal processing for meshes
Guskov, I., Sweldens, W., & Schröder, P. (1999) · Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99 · doi:10.1145/311535.311577 · Cited by 489
Marsden, J. E., & Hirani, A. N. (2003) · arXiv (Cornell University) · doi:10.7907/zhy8-v329 · Cited by 472
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry
Levy, B. (2006) · IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06) · doi:10.1109/smi.2006.21 · Cited by 422
Nealen, A., Igarashi, T., Sorkine, O., & Alexa, M. (2006) · Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia · doi:10.1145/1174429.1174494 · Cited by 340
Cited by
Kim, J. P., Kim, J., Park, Y. H., Park, S. B., Lee, J. S., Yoo, S., Kim, E.-J., Kim, H. J., Na, D. L., Brown, J. A., et al. (2019) · NeuroImage: Clinical · doi:10.1016/j.nicl.2019.101811 · Cited by 100
Kim, H.-J., Shin, J.-H., Han, C. E., Kim, H. J., Na, D. L., Seo, S. W., & Seong, J.-K. (2016) · Frontiers in Neuroscience · doi:10.3389/fnins.2016.00394 · Cited by 44
Metadata
- Authors
- Vallet, B., & Lévy, B.
- Venue
- Computer Graphics Forum
- Publisher
- Wiley
- Published
- 2008-04
- Volume
- 27
- Issue
- 2
- Pages
- 251-260
- ISSN
- 0167-7055 (ISSN-L)
- 1467-8659
- OpenAlex
- W1994393928
- Cited by
- 386
- References
- 22
- FWCI
- 26.61
- Type
- journal article
- Language
- en
- Open access
- green
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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.
