Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation (English)

in Eurographics Symposium on Geometry Processing ; 225-233
Eurographics Symposium on Geometry Processing
The Eurographics Association , Postfach 8043, 38621 Goslar, Germany; 2007

A deformation invariant representation of surfaces, the GPS embedding, is introduced using the eigenvalues and eigenfunctions of the Laplace-Beltrami differential operator. Notably, since the definition of the GPS embedding completely avoids the use of geodesic distances, and is based on objects of global character, the obtained representation is robust to local topology changes. The GPS embedding captures enough information to handle various shape processing tasks as shape classification, segmentation, and correspondence. To demonstrate the practical relevance of the GPS embedding, we introduce a deformation invariant shape descriptor called G2-distributions, and demonstrate their discriminative power, invariance under natural deformations, and robustness.

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Document information

  • Title:
    Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation
  • Author / Creator:
  • Page:
    225-233
  • Publisher:
    The Eurographics Association
  • Place of publication:
    Postfach 8043, 38621 Goslar, Germany
  • Year of publication:
    2007
  • Size:
    9 pages
  • ISBN:
  • ISSN:
  • DOI:
  • Type of media:
    Conference paper
  • Type of material:
    Electronic Resource
  • Language:
    English

Table of contents conference proceedings

The table of contents of the conference proceedings is generated automatically, so it can be incomplete, although all articles are available in the TIB.

13
Robust Statistical Estimation of Curvature on Discretized Surfaces
Kalogerakis, Evangelos / Simari, Patricio / Nowrouzezahrai, Derek / Singh, Karan | 2007
23
Focal Surfaces of Discrete Geometry
Yu, Jingyi / Yin, Xiaotian / Gu, Xianfeng / McMillan, Leonard / Gortler, Steven | 2007
33
Discrete Laplace operators: No free lunch
Wardetzky, Max / Mathur, Saurabh / Kaelberer, Felix / Grinspun, Eitan | 2007
39
Voronoi-based Variational Reconstruction of Unoriented Point Sets
Alliez, Pierre / Cohen-Steiner, David / Tong, Yiying / Desbrun, Mathieu | 2007
49
Reconstruction of Deforming Geometry from Time-Varying Point Clouds
Wand, Michael / Jenke, Philipp / Huang, Qixing / Bokeloh, Martin / Guibas, Leonidas / Schilling, Andreas | 2007
59
Data-Dependent MLS for Faithful Surface Approximation
Lipman, Yaron / Cohen-Or, Daniel / Levin, David | 2007
69
Multilevel Streaming for Out-of-Core Surface Reconstruction
Bolitho, Matthew / Kazhdan, Michael / Burns, Randal / Hoppe, Hugues | 2007
79
A Streaming Algorithm for Surface Reconstruction
Allegre, Remi / Chaine, Raphaelle / Akkouche, Samir | 2007
89
Shape Reconstruction from Unorganized Cross-sections
Boissonnat, Jean-Daniel / Memari, Pooran | 2007
99
Elastic Secondary Deformations by Vector Field Integration
Funck, Wolfram von / Theisel, Holger / Seidel, Hans-Peter | 2007
109
As-Rigid-As-Possible Surface Modeling
Sorkine, Olga / Alexa, Marc | 2007
117
GPU-assisted Positive Mean Value Coordinates for Mesh Deformations
Lipman, Yaron / Kopf, Johannes / Cohen-Or, Daniel / Levin, David | 2007
125
Unconstrained Isosurface Extraction on Arbitrary Octrees
Kazhdan, Michael / Klein, Allison / Dalal, Ketan / Hoppe, Hugues | 2007
135
Linear Angle Based Parameterization
Zayer, Rhaleb / Levy, Bruno / Seidel, Hans-Peter | 2007
143
Triangulations with Locally Optimal Steiner Points
Erten, Hale / Uengoer, Alper | 2007
153
Example-Based Skeleton Extraction
Schaefer, Scott / Yuksel, Can | 2007
163
Developable Surfaces from Arbitrary Sketched Boundaries
Rose, Kenneth / Sheffer, Alla / Wither, Jamie / Cani, Marie-Paule / Thibert, Boris | 2007
173
Dynamic Geometry Registration
Mitra, Niloy J. / Floery, Simon / Ovsjanikov, Maks / Gelfand, Natasha / Guibas, Leonidas / Pottmann, Helmut | 2007
183
Generalized Surface Flows for Mesh Processing
Eckstein, Ilya / Pons, Jean-Philippe / Tong, Yiying / Kuo, C.-C. Jay / Desbrun, Mathieu | 2007
193
Shape Optimization Using Reflection Lines
Tosun, Elif / Gingold, Yotam I. / Reisman, Jason / Zorin, Denis | 2007
203
Constraint-based Fairing of Surface Meshes
Hildebrandt, Klaus / Polthier, Konrad | 2007
213
Bayesian Surface Reconstruction via Iterative Scan Alignment to an Optimized Prototype
Huang, Qi-Xing / Adams, Bart / Wand, Michael | 2007
225
Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation
Rustamov, Raif M. | 2007
235
Symmetry-Enhanced Remeshing of Surfaces
Podolak, Joshua / Golovinskiy, Aleksey / Rusinkiewicz, Szymon | 2007
243
Ridge Based Curve and Surface Reconstruction
Suessmuth, Jochen / Greiner, Guenther | 2007
253
Surface Reconstruction using Local Shape Priors
Gal, Ran / Shamir, Ariel / Hassner, Tal / Pauly, Mark / Or, Daniel Cohen | 2007
263
Fast Normal Vector Compression with Bounded Error
Griffith, E. J. / Koutek, M. / Post, Frits H. | 2007
273
Delaunay Mesh Construction
Dyer, Ramsay / Zhang, Hao / Moeller, Torsten | 2007

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