Symmetry in 3D Geometry: Extraction and Applications

By Niloy J. Mitra, Mark Pauly, Michael Wand, Duygu Ceylan. 2013

387 citations recorded by the source corpus.

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, extract, encode and exploit geometric symmetries and 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 key 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 processing 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.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

In Computer Vision and Pattern Recognition

Citations in the corpus

VConv-DAE: Deep Volumetric Shape Learning Without Object Labels (2016, methodology): “A comprehensive survey of such techniques is covered in Mitra et al. [9].”
Data-driven structural priors for shape completion (2015, background): “While available symmetry detection algorithms assume a nearly complete shape [Mitra et al. 2013], Sipiran et al. [2014] focus on leveraging local features to handle larger occluded regions, yet, their method still requires some repeated structures to be visible.”
PCN: Point Completion Network (2018, methodology): “Symmetry-driven methods [29, 30, 35, 36, 46, 52, 55] identify symmetry axes and repeating regular structures in the partial input in order to copy parts from observed regions to unobserved regions.”
Learning to group discrete graphical patterns (2017, neutral): “Many techniques have been developed for exact and approximate symmetry detection of patterns found in natural images and shapes, e.g., [Barnes et al. 2010; Graham et al. 2010; Lukac et al. 2017; Podolak et al. 2006]; see also surveys by [Liu et al. 2010; Mitra et al. 2012].”
SceneGrok (2014, methodology): “This work introduced the concept of human-centric interactions to the shape analysis literature which targets higher-level understanding of both shape collections [Mitra et al. 2013a; Mitra et al. 2013b] and 3D scenes [Fisher et al. 2011].”
A Symmetry Prior for Convex Variational 3D Reconstruction (2016, background): “The works by Liu et al. [13] and Mitra et al. [16] give a broad overview of symmetry detection methods, although most of the work they discuss focuses on symmetry extraction for computer graphics applications.”