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Gaussian-product subdivision surfaces

Authors:

Reinhold Preiner,

Tamy Boubekeur,

Michael WimmerAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 38, Issue 4

Article No.: 35, Pages 1 - 11

https://doi.org/10.1145/3306346.3323026

Published: 12 July 2019 Publication History

Abstract

Probabilistic distribution models like Gaussian mixtures have shown great potential for improving both the quality and speed of several geometric operators. This is largely due to their ability to model large fuzzy data using only a reduced set of atomic distributions, allowing for large compression rates at minimal information loss. We introduce a new surface model that utilizes these qualities of Gaussian mixtures for the definition and control of a parametric smooth surface. Our approach is based on an enriched mesh data structure, which describes the probability distribution of spatial surface locations around each vertex via a Gaussian covariance matrix. By incorporating this additional covariance information, we show how to define a smooth surface via a nonlinear probabilistic subdivision operator based on products of Gaussians, which is able to capture rich details at fixed control mesh resolution. This entails new applications in surface reconstruction, modeling, and geometric compression.

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Cited By

Liang YHe FZeng XLuo J(2021)An improved Loop subdivision to coordinate the smoothness and the number of faces via multi-objective optimizationIntegrated Computer-Aided Engineering10.3233/ICA-210661(1-19)Online publication date: 23-Jul-2021
https://doi.org/10.3233/ICA-210661
Li YKamil SJacobson AGingold Y(2021)I♥LAACM Transactions on Graphics10.1145/3478513.348050640:6(1-14)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480506
Shi YNi BLiu JRong DQian YZhang W(2021)Geometric Granularity Aware Pixel-to-Mesh2021 IEEE/CVF International Conference on Computer Vision (ICCV)10.1109/ICCV48922.2021.01285(13077-13086)Online publication date: Oct-2021
https://doi.org/10.1109/ICCV48922.2021.01285
Show More Cited By

Index Terms

Gaussian-product subdivision surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Mesh geometry models
      2. Parametric curve and surface models
  2. Machine learning
    1. Machine learning approaches
      1. Learning in probabilistic graphical models
        Mixture models

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Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 38, Issue 4

August 2019

1480 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3306346

Editor:
Olga Sorkine-Hornung
ETH Zurich

Issue’s Table of Contents

Copyright © 2019 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 July 2019

Published in TOG Volume 38, Issue 4

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Cited By

Liang YHe FZeng XLuo J(2021)An improved Loop subdivision to coordinate the smoothness and the number of faces via multi-objective optimizationIntegrated Computer-Aided Engineering10.3233/ICA-210661(1-19)Online publication date: 23-Jul-2021
https://doi.org/10.3233/ICA-210661
Li YKamil SJacobson AGingold Y(2021)I♥LAACM Transactions on Graphics10.1145/3478513.348050640:6(1-14)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480506
Shi YNi BLiu JRong DQian YZhang W(2021)Geometric Granularity Aware Pixel-to-Mesh2021 IEEE/CVF International Conference on Computer Vision (ICCV)10.1109/ICCV48922.2021.01285(13077-13086)Online publication date: Oct-2021
https://doi.org/10.1109/ICCV48922.2021.01285
Liu HKim VChaudhuri SAigerman NJacobson A(2020)Neural subdivisionACM Transactions on Graphics10.1145/3386569.339241839:4(124:1-124:16)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392418
Trettner PKobbelt L(2020)Fast and Robust QEF Minimization using Probabilistic QuadricsComputer Graphics Forum10.1111/cgf.1393339:2(325-334)Online publication date: 13-Jul-2020
https://doi.org/10.1111/cgf.13933

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