Spectral compression of mesh geometry

By Zachi Karni, Craig Gotsman. European Workshop on Computational Geometry, 2000

759 citations recorded by the source corpus.

We show how spectral methods may be applied to 3D mesh data to obtain compact representations. This is achieved by projecting the mesh geometry onto an orthonormal basis derived from the mesh topology. To reduce complexity, the mesh is partitioned into a number of balanced submeshes with minimal interaction, each of which are compressed independently. Our methods may be used for compression and progressive transmission of 3D content, and are shown to be vastly superior to existing methods using spatial techniques, if slight loss can be tolerated.

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

View Paper: https://www.semanticscholar.org/paper/8a231f5ea9edd363c64b0fbfd619f209dce69141

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Spatial adaption of robot trajectories based on laplacian trajectory editing (2015, background): “The Laplace–Beltrami operator is well-known in the computer graphics community where it is applied to deform (Botsch and Kobbelt 2004a; Sorkine and Cohen-Or 2004); classify (Luxburg 2007; Reuter et al. 2009) and compress (Karni and Gotsman 2000; Levy 2006) triangular surfaces meshes.”
Mesh Segmentation - A Comparative Study (2006, background): “Mesh segmentation has become an important and challenging problem in computer graphics, with applications in areas as diverse as modeling [7], metamorphosis [10, 35], compression [13], simplification [6], 3D shape retrieval [36, 29], collision detection [18], texture mapping [17] and skeleton extrac”
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids (2006, methodology): “Even though these discrete Laplacians have been used for, e.g. dimensionality reduction [5] or mesh compression [41], the introduction of our computation of the Laplace–Beltrami spectra of the underlying manifolds in the areas of geometric modeling—CAD in particular and in computer graphics in…”
A generalized grid connectivity–based parameterization for subsurface flow model calibration (2011, background): “Both grids have a constant three‐point connectivity structure to immediate neighbor cells except at boundaries; therefore, the Laplacian eigenvectors reduce to the DCT basis [Strang, 1999; Karni and Gotsman, 2000].”
Recent advances in compression of 3D meshes (2005, positive): “The latter point has already proven to be of crucial importance for applications related to visualization (see the concept of visual metric in [33, 57]).”
Technologies for 3D mesh compression: A survey (2005, methodology): “Table 3 Bitrates of progressive mesh coding algorithms, which are of the form ''geometry bitrate in bpv:connectivity bitrate in bpv (quantization resolutions in bits)'' O (v log 2 v):N/A Popovic and Hoppe [46] O (v log 2 v):N/A Taubin et al. [47] 7–10:20–40 (6) Pajarola and Rossignac [49] 7:12–15 (8”
Mesh parameterization: theory and practice (2007, neutral): “Many different applications can use these eigenfunctions (some of them replace the discrete Laplacian with a combinatorial Laplacian, that only takes the mesh connections into account) : • matrix re-ordering [Fiedler, 1973] and mesh re-ordering [Isenburg and Lindstrom, 2005] • mesh compression [Karn”
Differential Representations for Mesh Processing (2006, methodology): “The spectral method of [15] provides high compression ratios, since most of the energy is concentrated in the lowfrequency coefficients (the first α i ), and the high-frequency components add negligible weight.”
Fundamentals of spherical parameterization for 3D meshes (2003, methodology): “Eigenvalues and eigenvectors of the Tutte Laplacian of a graph are the cornerstone of spectral graph theory [Chung 1997], and have also been used for coding 3D mesh geometry [Karni and Gotsman 2000].”
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation (2009, methodology): “Spectral methods have recently gained much interest in computer graphics [62], with applications that include mesh compression [30], parametrization [25,43], segmentation[31,35], remeshing [17], filtering [34,57],”
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry (2006, methodology): “This was used in [18] to define a compact encoding of mesh geometry.”
Segmentation of 3D meshes through spectral clustering (2004, background): “In spectral mesh compression [11] and watermarking [20], a large mesh is first decomposed into many small patches so that the cost of computing the eigenvectors becomes manageable.”
Mesh segmentation using feature point and core extraction (2005, methodology): “Cutting up a mesh into simpler sub-meshes benefits many algorithms in computer graphics, in areas as diverse as modeling [8], metamorphosis [11, 36], compression [14], simplification [10], 3D shape retrieval [37], collision detection [22], texture mapping [21], and skeleton extraction [15].”