Spectral Mesh Processing

By Bruno Lévy, Hao Zhang. International Conference on Computer Graphics and Interactive Techniques, 2009

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Spatial adaption of robot trajectories based on laplacian trajectory editing (2015, background): “The second condition is necessary as combinatorial mesh Laplacians do not take into account the geometry of the graph and thus rely on a regular mesh structure ( for a good approximation (Taubin 1995; Botsch and Kobbelt 2004b; Wardetzky et al. 2007).”
Reconstruction of Personalized 3D Face Rigs from Monocular Video (2016, methodology): “The eigenvectors are efficiently computed using the band-by-band shift invert spectral transform [Vallet and Lévy 2008; Lévy and Zhang 2010].”
GWCNN: A Metric Alignment Layer for Deep Shape Analysis (2017, unknown): “Spectral methods [ZvKD10] usually rely on the ﬁrst few eigenfunctions of a Laplacian operator and thus only encode low-frequency attributes of shapes.”
DiffusionNet: Discretization Agnostic Learning on Surfaces (2020, methodology): “In geometry processing, spectral methods have been used for a range of tasks including multi-resolution representation [Levy 2006], segmentation [Rustamov 2007] and matching [Ovsjanikov et al. 2012], among others [Vallet and Lévy 2008; Zhang et al. 2010].”