Symmetry in 3D Geometry: Extraction and Applications
Niloy J. Mitra, Mark Pauly, Michael Wand, Duygu Ceylan
State-of-the-art Report EUROGRAPHICS 2012


The concept of symmetry has received significant attention in computer graphics and computer vision research in recent years. Numerous methods have been proposed to find and extract geometric symmetries and exploit such high-level structural information for a wide variety of geometry processing tasks. This report surveys and classifies recent developments in symmetry detection. We focus on elucidating the similarities and differences between existing methods to gain a better understanding of a fundamental problem in digital geometry processing and shape understanding in general. We discuss a variety of applications in computer graphics and geometry that benefit from symmetry information for more effective processing. An analysis of the strengths and limitations of existing algorithms highlights the plenitude of opportunities for future research both in terms of theory and applications.

Acknowledgements :

We thank the Hao (Richard) Zhang and the reviewers for their helpful comments, and the various authors for images from their original papers. This research has been supported by the Marie Curie Career Integration Grant 303541 and the ERC Starting Grant 257453 COSYM.


AUTHOR = "Niloy J. Mitra and Mark Pauly and Michael Wand and Duygu Ceylan",
title = "Symmetry in 3D Geometry: Extraction and Applications",   
booktitle = "EUROGRAPHICS State-of-the-art Report", 
url = {},
doi = {10.1111/cgf.12010},
YEAR = "2012",

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