Anisotropic geometric diffusion in surface processing

By Ulrich Clarenz, Udo Diewald, Martin Rumpf. Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145), 2000

366 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1f40bc3cc041b571af11d859f1151bd2b896c89c

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds (2002, background): “Dierent forms of anisotropic diffusion have shown good results for this problem in image processing [PM90], in flow visualization [PR99], and more recently on meshes too [ CDR00 ].”
Anisotropic Laplace-Beltrami Operators for Shape Analysis (2014, positive): “discrete exterior calculus may be employed for this step [10], finite elements are a common tool to discretize differential operators, and have been applied with success to anisotropic operators [6].”
Interactive and anisotropic geometry processing using the screened Poisson equation (2011, methodology): “…the filtering of mesh geometry can be expressed in terms of the solution to a Poisson equation [Pinkall and Polthier 1993; Taubin 1995; Desbrun et al. 1999] and that geometry-awareness can be incorporated by anisotropically weighting the Laplace operator [Clarenz et al. 2000; Tasdizen et al. 2002].”
Robust moving least-squares fitting with sharp features (2005, methodology): “Our work is related to recent developments in feature-preserving smoothing [Clarenz et al. 2000; Fleishman et al. 2003b; Jones et al. 2003] but unlike smoothing, we define a surface rather than filtering the geometry.”
An Application of Markov Random Fields to Range Sensing (2005, background): “This includes work on diffusion processes [6], frequency-domain filtering [17], and anisotropic diffusion [5]; see also [3] and [1].”
Fast and Effective Feature-Preserving Mesh Denoising (2007, background): “In many cases, a single pass of a one-step or two-step approach does not yield a satisfactory result, and iterated operations are performed.”
Anisotropic diffusion of surfaces and functions on surfaces (2003, methodology): “) This was extended to smoothing or fairing noisy surfaces (see Clarenz et al. [2000], and Desbrun et al. [2000a,c]). For a surface M , the counterpart of the Laplacian 1 is the Laplace–Beltrami operator 1M (see do Carmo [1992]). One then obtains the geometric diffusion equation ∂t x −1M x = 0 for s”