An Optimisation-Based Approach to Mesh Smoothing: Reformulation and Extensions

Authors:
Yskandar Hamam;Michel Couprie
Affiliations:
F'SATIE at Tshwane University of Technology, Pretoria, RSA, and ESIEE, France;Université Paris-Est, Laboratoire d'Informatique Gaspard Monge, Equipe A3SI, ESIEE,
Venue:
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Year:
2009

Citing 15
Cited 3

A constrained optimization approach to finite element mesh smoothing

Finite Elements in Analysis and Design
A signal processing approach to fair surface design

SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Mesh Smoothing Using A Posteriori Error Estimates

SIAM Journal on Numerical Analysis
Optimal point placement for mesh smoothing

Journal of Algorithms
Implicit fairing of irregular meshes using diffusion and curvature flow

Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A Parallel Algorithm for Mesh Smoothing

SIAM Journal on Scientific Computing
Geometric surface smoothing via anisotropic diffusion of normals

Proceedings of the conference on Visualization '02
Polyhedral Surface Smoothing with Simultaneous Mesh Regularization

GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Mesh Smoothing via Mean and Median Filtering Applied to Face Normals

GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Curve and surface smoothing without shrinkage

ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Bilateral mesh denoising

ACM SIGGRAPH 2003 Papers
A Global Laplacian Smoothing Approach with Feature Preservation

CAD-CG '05 Proceedings of the Ninth International Conference on Computer Aided Design and Computer Graphics
Triangular surface mesh fairing via Gaussian curvature flow

Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Laplacian mesh optimization

Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Discrete regularization on weighted graphs for image and mesh filtering

SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision

Grid smoothing: a graph-based approach

CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
Correction of atmospheric turbulence degraded sequences using grid smoothing

ICIAR'11 Proceedings of the 8th international conference on Image analysis and recognition - Volume Part II
Bilateral mesh filtering

Pattern Recognition Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Laplacian approach, when applied to mesh smoothing leads in many cases to convergence problems. It also leads to shrinking of the mesh. In this work, the authors reformulate the mesh smoothing problem as an optimisation one. This approach gives the means of controlling the steps to assure monotonic convergence. Furthermore, a new optimisation function is proposed that reduces the shrinking effect of the method. Examples are given to illustrate the properties of the proposed approches.