SIGGRAPH 2010 course

Spectral mesh processing was proposed at the beginning of the 1990s to port the “signal processing toolbox” to 3D mesh models. Now, with recent advances in computing power and numerical software, this vision can be fully implemented. In this course, attendees learn how to transfer the underlying concepts to the mesh-model setting, how to implement the “spectral mesh processing” toolbox, and how to use it for real applications, including filtering, shape matching, remeshing, segmentation, and parameterization.

A previous version of this course was also given at SIGGRAPH ASIA 2009 in Yokohama, Japan.

Presenters

• Bruno Lévy (INRIA)
• Hao (Richard) Zhang (Simon Fraser University)

Course notes

• http://alice.loria.fr/publications/papers/2010/spectral_course/spectral_course.pdf

Slides

• Introduction (Levy)
• What is so Spectral? (Zhang)
• Do your own Spectral Mesh Processing at home (Levy)
• Applications: Segmentation, Correspondence, Retrieval, Symmetry Detection (Zhang)
• Applications: Parameterization, Remeshing, Quadragulation, Heat Kernels (Levy)

Programming / source code

• Graphite software tutorial: Spectral geometry processing with ManifoldHarmonics (also has spectral conformal parameterization)

Further reading

• Our book Polygon Mesh Processing (Botsch, Kobbelt, Pauly, Alliez and Levy, AK Peters), chapter 4 (Smoothing, Fourier Transform and Manifold Harmonics, Diffusion Flow, Fairing, ...)
• Survey paper on spectral mesh processing
• Part-aware metric paper from Eurographics 2009
• Manifold harmonics I (derivation in DEC)
• Manifold harmonics II (derivation in FEM)
• Spectral mesh segmentation paper from Eurographics 2007
• Laplacian Eigenfunctions paper at SMI 2006
• Spectral non-rigid shape correspondence paper from SMI 2006
• Spectral shape retrieval paper in CAD journal (2010 Most Cited Paper Award for the journal Computer-Aided Design)
• Yves Colin de Verdiere's webpage (nice tutorials in French about spectral graph theory)