research-article

Fuzzy Vector Median-Based Surface Smoothing

Authors:

Kenneth E. BarnerAuthors Info & Claims

IEEE Transactions on Visualization and Computer Graphics, Volume 10, Issue 3

Pages 252 - 265

https://doi.org/10.1109/TVCG.2004.1272725

Published: 01 May 2004 Publication History

Abstract

Abstract--This paper proposes a novel approach for smoothing surfaces represented by triangular meshes. The proposed method is a two-step procedure: surface normal smoothing through fuzzy vector median (FVM) filtering followed by integration of surface normals for vertex position update based on the least square error (LSE) criteria. Median and Order Statistic-based filters are extensively used in signal processing, especially image processing, due to their ability to reject outliers and preserve features such as edges and monotonic regions. More recently, fuzzy ordering theory has been introduced to allow averaging among similarly valued samples. Fuzzy ordering theory leads naturally to the fuzzy median, which yields improved noise smoothing over traditional crisp median filters. This paper extends the fuzzy ordering concept to vector-based data and introduces the fuzzy vector median filter. The application of FVM filters to surface normal smoothing yields improved results over previously introduced normal smoothing algorithms. The improved filtering results, coupled with LSE vertex position update, produces surface smoothing that minimizes the effects of noise while simultaneously preserving detail features. The proposed method is simple to implement and relatively fast. Simulation results are presented showing the performance of the proposed method and its advantages over commonly used surface smoothing algorithms. Additionally, optimization procedures for FVM filters are derived and evaluated.

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Cited By

Cui RGæde ERotenberg EKobbelt LBærentzen J(2024)Surface Reconstruction Using Rotation SystemsACM Transactions on Graphics10.1145/368795643:6(1-22)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687956
Wang XZhang XCui WXiong RFan XZhao DCai JKankanhalli MPrabhakaran BBoll SSubramanian RZheng LSingh VCesar PXie LXu D(2024)Mesh Denoising Using Filtering Coefficients Jointly Aware of Noise and GeometryProceedings of the 32nd ACM International Conference on Multimedia10.1145/3664647.3681143(1791-1799)Online publication date: 28-Oct-2024
https://dl.acm.org/doi/10.1145/3664647.3681143
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
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Index Terms

Fuzzy Vector Median-Based Surface Smoothing
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics Volume 10, Issue 3

May 2004

128 pages

ISSN:1077-2626

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Copyright © Copyright © 2004 IEEE. All Rights Reserved.

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IEEE Educational Activities Department

United States

Publication History

Published: 01 May 2004

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Cited By

Cui RGæde ERotenberg EKobbelt LBærentzen J(2024)Surface Reconstruction Using Rotation SystemsACM Transactions on Graphics10.1145/368795643:6(1-22)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687956
Wang XZhang XCui WXiong RFan XZhao DCai JKankanhalli MPrabhakaran BBoll SSubramanian RZheng LSingh VCesar PXie LXu D(2024)Mesh Denoising Using Filtering Coefficients Jointly Aware of Noise and GeometryProceedings of the 32nd ACM International Conference on Multimedia10.1145/3664647.3681143(1791-1799)Online publication date: 28-Oct-2024
https://dl.acm.org/doi/10.1145/3664647.3681143
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
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
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Smolka BKusnik D(2020)On the application of the reachability distance in the suppression of mixed Gaussian and impulsive noise in color imagesMultimedia Tools and Applications10.1007/s11042-020-09550-w79:43-44(32857-32879)Online publication date: 1-Nov-2020
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Prez-Benito CMorillas SJordn CConejero J(2018)A model based on local graphs for colour images and its application for Gaussian noise smoothingJournal of Computational and Applied Mathematics10.1016/j.cam.2017.05.013330:C(955-964)Online publication date: 1-Mar-2018
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Chen HShen J(2018)Denoising of point cloud data for computer-aided design, engineering, and manufacturingEngineering with Computers10.1007/s00366-017-0556-434:3(523-541)Online publication date: 1-Jul-2018
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Wang PLiu YTong X(2016)Mesh denoising via cascaded normal regressionACM Transactions on Graphics10.1145/2980179.298023235:6(1-12)Online publication date: 5-Dec-2016
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