Foundations and Trends® in Computer Graphics and Vision > Vol 5 > Issue 1–2

Computational Symmetry in Computer Vision and Computer Graphics

Yanxi Liu, Pennsylvania State University, USA, yanxi@cse.psu.edu Hagit Hel-Or, University of Haifa, Israel, hagit@cs.haifa.ac.il Craig S. Kaplan, University of Waterloo, Canada, csk@uwaterloo.ca Luc Van Gool, KU Leuven, Belgium and ETH Zurich, Switzerland, Luc.Vangool@esat.kuleuven.ac.be
 
Suggested Citation
Yanxi Liu, Hagit Hel-Or, Craig S. Kaplan and Luc Van Gool (2010), "Computational Symmetry in Computer Vision and Computer Graphics", Foundations and Trends® in Computer Graphics and Vision: Vol. 5: No. 1–2, pp 1-195. http://dx.doi.org/10.1561/0600000008

Published: 04 Aug 2010
© 2010 Y. Liu, H. Hel-Or, C. S. Kaplan and L. Van Gool
 
Subjects
Learning and statistical methods
 

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In this article:
1. Introduction
2. Symmetry and Symmetry Groups
3. Symmetry Detection
4. Near Regular Texture (NRT)
5. Continuous Symmetry
6. Symmetry in Graphics
7. Summary
Acknowledgements
References

Abstract

In the arts and sciences, as well as in our daily lives, symmetry has made a profound and lasting impact. Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences. Though the term computational symmetry was formally defined a decade ago by the first author, referring to algorithmic treatment of symmetries, seeking symmetry from digital data has been attempted for over four decades. Computational symmetry on real world data turns out to be challenging enough that, after decades of effort, a fully automated symmetry–savvy system remains elusive for real world applications. The recent resurging interests in computational symmetry for computer vision and computer graphics applications have shown promising results. Recognizing the fundamental relevance and potential power that computational symmetry affords, we offer this survey to the computer vision and computer graphics communities. This survey provides a succinct summary of the relevant mathematical theory, a historic perspective of some important symmetry-related ideas, a partial yet timely report on the state of the arts symmetry detection algorithms along with its first quantitative benchmark, a diverse set of real world applications, suggestions for future directions and a comprehensive reference list.

DOI:10.1561/0600000008
ISBN: 978-1-60198-364-0
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Table of contents:
1. Introduction
2. Symmetry and Symmetry Groups
3. Symmetry Detection
4. Near Regular Texture (NRT)
5. Continuous Symmetry
6. Symmetry in Graphics
7. Summary
Acknowledgments
References

Computational Symmetry in Computer Vision and Computer Graphics

In the arts and sciences, as well as in our daily lives, symmetry has made a profound and lasting impact. Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences. Though the term Computational Symmetry was formally defined a decade ago, referring to algorithmic treatment of symmetries, seeking symmetry from digital data has been attempted for over four decades. Computational symmetry on real world data turns out to be challenging enough that, after decades of effort, a fully automated symmetry-savvy system remains elusive for real world applications.

Computational Symmetry in Computer Vision and Computer Graphics provides a succinct summary of the relevant mathematical theory, a historic perspective of some important symmetry-related ideas, a partial yet timely report on the state of the arts symmetry detection algorithms along with its first quantitative benchmark, a diverse set of real world applications, suggestions for future directions and a comprehensive reference list. The recent resurgence in interest in computational symmetry for computer vision and computer graphics applications has shown promising results.

Computational Symmetry in Computer Vision and Computer Graphics illustrates how far we have come and where the future challenges and opportunities may lie.

 
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