article

Anisotropic diffusion of surfaces and functions on surfaces

Authors:

Chandrajit L. Bajaj,

Guoliang XuAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 22, Issue 1

Pages 4 - 32

https://doi.org/10.1145/588272.588276

Published: 01 January 2003 Publication History

Abstract

We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated two-manifold surface meshes in IR³ and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combine the C¹ limit representation of Loop's subdivision for triangular surface meshes and vector functions on the surface mesh with the established diffusion model to arrive at a discretized version of the diffusion problem in the spatial direction. The time direction discretization then leads to a sparse linear system of equations. Iteratively solving the sparse linear system yields a sequence of faired (smoothed) meshes as well as faired functions.

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Liu YWu CZeng C(2024)Non-Lipschitz Variational Models and their Iteratively Reweighted Least Squares Algorithms for Image Denoising on SurfacesSIAM Journal on Imaging Sciences10.1137/23M159439X17:2(1255-1283)Online publication date: 20-Jun-2024
https://doi.org/10.1137/23M159439X
Hurtado JGattass MRaposo ALopez C(2024)Sharp feature-preserving mesh denoisingMultimedia Tools and Applications10.1007/s11042-024-18390-x83:27(69555-69580)Online publication date: 1-Feb-2024
https://doi.org/10.1007/s11042-024-18390-x
Yang BRen HZuo TLiu Z(2023)A Stream Function Smoothing Method for the Design of MRI Gradient Coils on Non-Developable SurfacesSensors10.3390/s2318791223:18(7912)Online publication date: 15-Sep-2023
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Index Terms

Anisotropic diffusion of surfaces and functions on surfaces
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
  2. Computer graphics
    1. Image manipulation
      1. Texturing
    2. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
  2. Probability and statistics
    1. Probabilistic representations
      1. Nonparametric representations
        Spline models

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 22, Issue 1

January 2003

129 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/588272

Issue’s Table of Contents

Copyright © 2003 ACM.

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Publication History

Published: 01 January 2003

Published in TOG Volume 22, Issue 1

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Cited By

Liu YWu CZeng C(2024)Non-Lipschitz Variational Models and their Iteratively Reweighted Least Squares Algorithms for Image Denoising on SurfacesSIAM Journal on Imaging Sciences10.1137/23M159439X17:2(1255-1283)Online publication date: 20-Jun-2024
https://doi.org/10.1137/23M159439X
Hurtado JGattass MRaposo ALopez C(2024)Sharp feature-preserving mesh denoisingMultimedia Tools and Applications10.1007/s11042-024-18390-x83:27(69555-69580)Online publication date: 1-Feb-2024
https://doi.org/10.1007/s11042-024-18390-x
Yang BRen HZuo TLiu Z(2023)A Stream Function Smoothing Method for the Design of MRI Gradient Coils on Non-Developable SurfacesSensors10.3390/s2318791223:18(7912)Online publication date: 15-Sep-2023
https://doi.org/10.3390/s23187912
Chen HLi ZWei MWang J(2023)Geometric and Learning-Based Mesh Denoising: A Comprehensive SurveyACM Transactions on Multimedia Computing, Communications, and Applications10.1145/362509820:3(1-28)Online publication date: 10-Nov-2023
https://dl.acm.org/doi/10.1145/3625098
Xiu HLiu XWang WKim KShinohara TChang QMatsuoka M(2023)Diffusion unitNeurocomputing10.1016/j.neucom.2023.126780559:COnline publication date: 28-Nov-2023
https://dl.acm.org/doi/10.1016/j.neucom.2023.126780
Liu BLi BCao JWang WLiu X(2023)Adaptive and propagated mesh filteringComputer-Aided Design10.1016/j.cad.2022.103422154(103422)Online publication date: Jan-2023
https://doi.org/10.1016/j.cad.2022.103422
Xing YTan JHong PHe YHu M(2022)Mesh Denoising Based on Recurrent Neural NetworksSymmetry10.3390/sym1406123314:6(1233)Online publication date: 14-Jun-2022
https://doi.org/10.3390/sym14061233
Shen YFu HDu ZChen XBurnaev EZorin DZhou KZheng Y(2022)GCN-Denoiser: Mesh Denoising with Graph Convolutional NetworksACM Transactions on Graphics10.1145/348016841:1(1-14)Online publication date: 9-Feb-2022
https://dl.acm.org/doi/10.1145/3480168
Zhang HHe ZWang X(2022)A Novel Mesh Denoising Method Based on Relaxed Second-Order Total Generalized VariationSIAM Journal on Imaging Sciences10.1137/21M139794515:1(1-22)Online publication date: 4-Jan-2022
https://doi.org/10.1137/21M1397945
Wang FZhu DXie HWang WCheng G(2022)Three-dimensional surface mesh optimization and centerline extraction of vasculatures for endovascular intervention simulationJournal of Electronic Imaging10.1117/1.JEI.31.3.03303831:03Online publication date: 1-May-2022
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