Spectral Geometry Processing with Manifold Harmonics

By B. Vallet, Bruno Lévy. Computer graphics forum (Print), 2008

447 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/43c3a4a1057f3b6df764611cc17d4daf3d9e1997

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

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].”
Mesh parameterization: theory and practice (2007, background): “to arbitrary manifolds, this function basis is naturally called the Manifold Harmonics Basis (MHB) [Vallet and Lévy, 2007].”
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].”
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation (2009, methodology): “jtij is the area of the triangle ti, and t1, t2 are the triangles that share the edge ði; jÞ, and Acot is the stiffness matrix with cotangent weights (see also [34,58]).”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, methodology): “Our work is inspired in large part by the recent development of spectral methods for geometry processing, data and shape analysis, and shape, graph and data matching [7,18–33].”
State of the Art on Monocular 3D Face Reconstruction, Tracking, and Applications (2018, background): “Bouaziz et al. [BWP13] proposed the use of a medium-scale corrective basis, which is based on manifold harmonics [VL08].”
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment (2016, background): “…we wish for the development of a ‘shape ﬁltering’ theory, according to which suitable functions concur to model shape properties of interest, playing at the same time the role of manifold harmonics in geometric ﬁltering [VL08], that is, enabling a progressive, ‘property-based’ shape representation.”
Laplace-Beltrami eigenfunctions for deformation invariant shape representation (2007, unknown): “Vallet and Levy [VL07] use the Finite Element Method to explain the root of this inconsistency.”
Self-Supervised Multi-level Face Model Learning for Monocular Reconstruction at Over 250 Hz (2017, background): “[12] introduced medium-scale shape correctives based on manifold harmonics [65].”