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Symmetry in 3D Geometry: Extraction and Applications

Identifieur interne : 000141 ( Main/Exploration ); précédent : 000140; suivant : 000142

Symmetry in 3D Geometry: Extraction and Applications

Auteurs : Niloy J. Mitra [Royaume-Uni] ; Mark Pauly [Suisse] ; Michael Wand [Allemagne] ; Duygu Ceylan [Suisse]

Source :

RBID : ISTEX:96BBF39F2DD0203B75DFC2CE969AED869D0F89E3

English descriptors

Abstract

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.
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.

Url:
DOI: 10.1111/cgf.12010


Affiliations:


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Le document en format XML

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<term>Algorithm</term>
<term>Allowable transformation</term>
<term>Approximate symmetries</term>
<term>Approximate symmetry</term>
<term>Approximation level</term>
<term>Attened meshes</term>
<term>Authors computer graphics forum</term>
<term>Base index</term>
<term>Base patch</term>
<term>Berner</term>
<term>Bius</term>
<term>Bokeloh</term>
<term>Bottom panel</term>
<term>Broader class</term>
<term>Bronstein</term>
<term>Brute force approach</term>
<term>Building blocks</term>
<term>Candidate transformations</term>
<term>Canonical</term>
<term>Centre</term>
<term>Classical theory</term>
<term>Closest function</term>
<term>Computational geometry</term>
<term>Computer</term>
<term>Computer graphics</term>
<term>Computer graphics forum</term>
<term>Computer vision</term>
<term>Continuous symmetry</term>
<term>Correspondence matrix</term>
<term>Corresponding euclidean distances</term>
<term>Corresponding point pairs</term>
<term>Curvature</term>
<term>Curvature extrema</term>
<term>Cyclic group</term>
<term>Descriptor</term>
<term>Detection</term>
<term>Different classes</term>
<term>Different parts</term>
<term>Different types</term>
<term>Dihedral</term>
<term>Dihedral group</term>
<term>Distance function</term>
<term>Distance measure</term>
<term>Docking sites</term>
<term>Eld</term>
<term>Elementary building block</term>
<term>Embedding</term>
<term>Encoding</term>
<term>Equilateral triangle</term>
<term>Equivalent points</term>
<term>Euclidean</term>
<term>Euclidean distance</term>
<term>Euclidean geometry</term>
<term>Euclidean symmetries</term>
<term>Euclidean symmetry detection</term>
<term>Eurographics</term>
<term>Eurographics association</term>
<term>Exact symmetries</term>
<term>Extrinsic</term>
<term>False positives</term>
<term>Feature curves</term>
<term>Feature descriptor</term>
<term>Feature lines</term>
<term>Feature points</term>
<term>Feature selection</term>
<term>Felix klein</term>
<term>Frieze groups</term>
<term>Funkhouser</term>
<term>Gaussian</term>
<term>Gaussian curvature</term>
<term>Gaussian image</term>
<term>Geodesic</term>
<term>Geometric data</term>
<term>Geometric data sets</term>
<term>Geometric hashing</term>
<term>Geometric information</term>
<term>Geometric models</term>
<term>Geometric object</term>
<term>Geometric objects</term>
<term>Geometric symmetries</term>
<term>Geometry</term>
<term>Geometry figure</term>
<term>Geometry processing</term>
<term>Global</term>
<term>Global image volume points mesh input disc</term>
<term>Global mirror symmetry</term>
<term>Global point signature</term>
<term>Global symmetries</term>
<term>Global symmetry</term>
<term>Global symmetry detection</term>
<term>Good model</term>
<term>Grand goal</term>
<term>Graphics</term>
<term>Grid</term>
<term>Group structure</term>
<term>Group theory</term>
<term>Guibas</term>
<term>Hash table</term>
<term>Hashing</term>
<term>Heat kernels</term>
<term>Hierarchical</term>
<term>Hierarchical encoding</term>
<term>Identity transformation</term>
<term>Ieee</term>
<term>Ieee transactions</term>
<term>Images courtesy</term>
<term>Information content</term>
<term>Information theory</term>
<term>Input scene</term>
<term>Input shape</term>
<term>International journal</term>
<term>Intrinsic</term>
<term>Intrinsic symmetries</term>
<term>Inverse element</term>
<term>Isometric</term>
<term>Isometric deformation</term>
<term>Isometric deformations</term>
<term>Isometric symmetry detection problem</term>
<term>Isometric transformations</term>
<term>Isometry</term>
<term>John wiley sons</term>
<term>Kazhdan</term>
<term>Laplace beltrami operators</term>
<term>Last step</term>
<term>Line features</term>
<term>Linear features</term>
<term>Lipman</term>
<term>Local evidence</term>
<term>Local features</term>
<term>Local geometry</term>
<term>Local neighbourhood</term>
<term>Local patches</term>
<term>Machine intelligence</term>
<term>Main stages</term>
<term>Many objects</term>
<term>Mesh</term>
<term>Mesh segmentation</term>
<term>Mesh vertices</term>
<term>Mitra</term>
<term>Model acquisition</term>
<term>Modeling</term>
<term>Natural choice</term>
<term>Neighbourhood</term>
<term>Nite</term>
<term>Nite point groups</term>
<term>Normal vector</term>
<term>Object centroid</term>
<term>Object parts</term>
<term>Other words</term>
<term>Ovsjanikov</term>
<term>Pairwise</term>
<term>Pairwise correspondences</term>
<term>Pairwise relations</term>
<term>Pairwise symmetries</term>
<term>Partial</term>
<term>Partial symmetries</term>
<term>Partial symmetry</term>
<term>Partial symmetry detection</term>
<term>Partial symmetry detection methods</term>
<term>Pattern analysis</term>
<term>Pauly</term>
<term>Perfect symmetry</term>
<term>Planar</term>
<term>Planar symmetry</term>
<term>Podolak</term>
<term>Point cloud data</term>
<term>Point clouds</term>
<term>Point pairs</term>
<term>Point sets</term>
<term>Possible choices</term>
<term>Potential symmetry candidates</term>
<term>Potential symmetry transformations</term>
<term>Potential transformations</term>
<term>Principal curvature directions</term>
<term>Principal curvatures</term>
<term>Proc</term>
<term>Procedural modeling</term>
<term>Prst</term>
<term>Query patch</term>
<term>Random sampling</term>
<term>Raviv</term>
<term>Recent years</term>
<term>Regular grid</term>
<term>Regularity</term>
<term>Regularity patterns</term>
<term>Repetitive patterns</term>
<term>Rigid transformation</term>
<term>Rigid transformations</term>
<term>Rotational symmetry</term>
<term>Sample points</term>
<term>Scan consolidation</term>
<term>Search space</term>
<term>Segmentation</term>
<term>Seidel</term>
<term>Shape analysis</term>
<term>Shape descriptor</term>
<term>Shape editing</term>
<term>Shape modeling</term>
<term>Shape variations</term>
<term>Siggraph</term>
<term>Siggraph asia</term>
<term>Signature space</term>
<term>Similar occurences</term>
<term>Similarity transformations</term>
<term>Small number</term>
<term>Source points</term>
<term>Spatial domain</term>
<term>Special case</term>
<term>Structural models</term>
<term>Structural redundancy</term>
<term>Structural regularity</term>
<term>Subset</term>
<term>Such boundaries</term>
<term>Surface correspondence</term>
<term>Surface geometry</term>
<term>Surface patch</term>
<term>Surface patches</term>
<term>Surface point</term>
<term>Symmetric</term>
<term>Symmetric parts</term>
<term>Symmetric patches</term>
<term>Symmetric pieces</term>
<term>Symmetric surfaces</term>
<term>Symmetry</term>
<term>Symmetry correspondence matrix</term>
<term>Symmetry descriptors</term>
<term>Symmetry detection</term>
<term>Symmetry detection algorithm</term>
<term>Symmetry detection algorithms</term>
<term>Symmetry detection methods</term>
<term>Symmetry detection problem</term>
<term>Symmetry distance</term>
<term>Symmetry group</term>
<term>Symmetry groups</term>
<term>Symmetry information</term>
<term>Symmetry properties</term>
<term>Symmetry relations</term>
<term>Symmetry transformation</term>
<term>Symmetry transformation space</term>
<term>Symmetry transformations</term>
<term>Target application</term>
<term>Trans</term>
<term>Transactions</term>
<term>Transformation</term>
<term>Transformation domain</term>
<term>Transformation groups</term>
<term>Transformation space</term>
<term>Triangle meshes</term>
<term>Various applications</term>
<term>Voting scheme</term>
<term>Wallpaper groups</term>
<term>Wand</term>
<term>Wide range</term>
<term>Wiley</term>
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<div type="abstract">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.</div>
<div type="abstract" xml:lang="en">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.</div>
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