Estimating 3-D rigid body transformations: a comparison of four major algorithms
Machine Vision and Applications - Special issue on performance evaluation
Using bilateral symmetry to improve 3D reconstruction from image sequences
Computer Vision and Image Understanding
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Geometric Hashing: An Overview
IEEE Computational Science & Engineering
Symmetry as a Continuous Feature
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Reflective Symmetry Descriptor
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
From curve design algorithms to the design of rigid body motions
The Visual Computer: International Journal of Computer Graphics
Symmetry descriptors and 3D shape matching
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
As-rigid-as-possible shape manipulation
ACM SIGGRAPH 2005 Papers
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Salient geometric features for partial shape matching and similarity
ACM Transactions on Graphics (TOG)
Accurate detection of symmetries in 3D shapes
ACM Transactions on Graphics (TOG)
A planar-reflective symmetry transform for 3D shapes
ACM SIGGRAPH 2006 Papers
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Example-based 3D scan completion
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
PriMo: coupled prisms for intuitive surface modeling
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Folding meshes: hierarchical mesh segmentation based on planar symmetry
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Partial matching of 3D shapes with priority-driven search
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
IEEE Transactions on Computers
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
Joint-aware manipulation of deformable models
ACM SIGGRAPH 2009 papers
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Digital anastylosis of the Octagon in Ephesos
Journal on Computing and Cultural Heritage (JOCCH)
A new possibility for pattern recognition independently from geometrical measuresetrical measures
ICOSSSE'08 Proceedings of the 7th WSEAS international conference on System science and simulation in engineering
Symmetry-Aware Mesh Processing
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Abstraction of man-made shapes
ACM SIGGRAPH Asia 2009 papers
Partial intrinsic reflectional symmetry of 3D shapes
ACM SIGGRAPH Asia 2009 papers
ACM SIGGRAPH Asia 2009 papers
Exploiting repeated patterns for efficient compression of massive models
Proceedings of the 8th International Conference on Virtual Reality Continuum and its Applications in Industry
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
Automatic registration for articulated shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
ACM SIGGRAPH 2010 papers
Paneling architectural freeform surfaces
ACM SIGGRAPH 2010 papers
NPAR '10 Proceedings of the 8th International Symposium on Non-Photorealistic Animation and Rendering
A survey on CAD methods in 3D garment design
Computers in Industry
A multiscale model for virus capsid dynamics
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Analysis, reconstruction and manipulation using arterial snakes
ACM SIGGRAPH Asia 2010 papers
Intrinsic regularity detection in 3D geometry
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Single viewpoint model completion of symmetric objects for digital inspection
Computer Vision and Image Understanding
Exploration of continuous variability in collections of 3D shapes
ACM SIGGRAPH 2011 papers
GlobFit: consistently fitting primitives by discovering global relations
ACM SIGGRAPH 2011 papers
Learning to compute the plane of symmetry for human faces
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
Symmetry-guided texture synthesis and manipulation
ACM Transactions on Graphics (TOG)
Shape palindromes: analysis of intrinsic symmetries in 2d articulated shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Factored Facade Acquisition using Symmetric Line Arrangements
Computer Graphics Forum
Finding Surface Correspondences Using Symmetry Axis Curves
Computer Graphics Forum
Shape-Up: Shaping Discrete Geometry with Projections
Computer Graphics Forum
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Structure recovery by part assembly
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Generative object definition and semantic recognition
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
A graph-based approach to symmetry detection
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
Transformed polynomials for global registration of point clouds
Proceedings of the 27th Spring Conference on Computer Graphics
Structure-aware shape processing
SIGGRAPH Asia 2013 Courses
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We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized point-pair mappings. We derive closed-form solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.