A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
CGI '00 Proceedings of the International Conference on Computer Graphics
Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Laplace spectra as fingerprints for image recognition
Computer-Aided Design
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Mass Density Laplace-Spectra for Image Recognition
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
Global Medical Shape Analysis Using the Volumetric Laplace Spectrum
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
ACM SIGGRAPH 2009 papers
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
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Inverse-Consistent Surface Mapping with Laplace-Beltrami Eigen-Features
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Global medical shape analysis using the Laplace-Beltrami spectrum
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
Spin transformations of discrete surfaces
ACM SIGGRAPH 2011 papers
Euclidean geodesic loops on high-genus surfaces applied to the morphometry of vestibular systems
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Eigenmodes of surface energies for shape analysis
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Robust Dense Registration of Partial Nonrigid Shapes
IEEE Transactions on Visualization and Computer Graphics
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Feature line extraction from unorganized noisy point clouds using truncated Fourier series
The Visual Computer: International Journal of Computer Graphics
SMI 2013: Laplacians on flat line bundles over 3-manifolds
Computers and Graphics
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Computing the spectral decomposition of the Laplace-Beltrami operator on a manifold M has proven useful for applications such as shape retrieval and geometry processing. The standard operator acts on scalar functions which can be identified with sections of the trivial line bundle MxR. In this work we propose to extend the discussion to Laplacians on nontrivial real line bundles. These line bundles are in one-to-one correspondence with elements of the first cohomology group of the manifold with Z"2 coefficients. While we focus on the case of two-dimensional closed surfaces, we show that our method also applies to surfaces with boundaries. Denoting by @b the rank of the first cohomology group, there are 2^@b different line bundles to consider and each of these has a naturally associated Laplacian that possesses a spectral decomposition. Using our new method it is possible for the first time to compute the spectra of these Laplacians by a simple modification of the finite element basis functions used in the standard trivial bundle case. Our method is robust and efficient. We illustrate some properties of the modified spectra and eigenfunctions and indicate possible applications for shape processing. As an example, using our method, we are able to create spectral shape descriptors with increased sensitivity in the eigenvalues with respect to geometric deformations and to compute cycles aligned to object symmetries in a chosen homology class.