article

Piecewise regular meshes: construction and compression

Authors:

Andrzej Szymczak,

Jarek Rossignac,

Davis KingAuthors Info & Claims

Graphical Models, Volume 64, Issue 3-4

Pages 183 - 198

https://doi.org/10.1006/gmod.2002.0577

Published: 01 May 2002 Publication History

Abstract

We present an algorithm which splits a 3D surface into reliefs, relatively fiat regions that have smooth boundaries. The surface is then resampled in a regular manner within each of the reliefs. As a result, we obtain a piecewise regular mesh (PRM) having a regular structure on large regions. Experimental results show that we are able to approximate the input surface with the mean square error of about 0.01- 0.02% of the diameter of the bounding box without increasing the number of vertices. We introduce a compression scheme tailored to work with our remeshed models and show that it is able to compress them losslessly (after quantizing the vertex locations) without significantly increasing the approximation error using about 4 bits per vertex of the resampled model.

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Cited By

von Buelow MGuthe SGoesele MHullin MKlein RSchultz TYao A(2017)Compression of non-manifold polygonal meshes revisitedProceedings of the conference on Vision, Modeling and Visualization10.2312/vmv.20171266(111-118)Online publication date: 25-Sep-2017
https://dl.acm.org/doi/10.2312/vmv.20171266
Maglo ALavoué GDupont FHudelot C(2015)3D Mesh CompressionACM Computing Surveys10.1145/269344347:3(1-41)Online publication date: 17-Feb-2015
https://dl.acm.org/doi/10.1145/2693443
Chihaoui MElkefi ABellil WBen Amar C(2015)Sphere-Tree Semi-regular RemesherProceedings of the 16th International Conference on Advanced Concepts for Intelligent Vision Systems - Volume 938610.1007/978-3-319-25903-1_71(826-837)Online publication date: 26-Oct-2015
https://dl.acm.org/doi/10.1007/978-3-319-25903-1_71
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Index Terms

Piecewise regular meshes: construction and compression
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Approximation algorithms
      2. Graph algorithms
  2. Mathematical analysis
    1. Quadrature

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Information

Published In

cover image Graphical Models

Graphical Models Volume 64, Issue 3-4

Special issue: Processing on large polygonal meshes

May/July 2002

113 pages

ISSN:1524-0703

Issue’s Table of Contents

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 May 2002

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Cited By

von Buelow MGuthe SGoesele MHullin MKlein RSchultz TYao A(2017)Compression of non-manifold polygonal meshes revisitedProceedings of the conference on Vision, Modeling and Visualization10.2312/vmv.20171266(111-118)Online publication date: 25-Sep-2017
https://dl.acm.org/doi/10.2312/vmv.20171266
Maglo ALavoué GDupont FHudelot C(2015)3D Mesh CompressionACM Computing Surveys10.1145/269344347:3(1-41)Online publication date: 17-Feb-2015
https://dl.acm.org/doi/10.1145/2693443
Chihaoui MElkefi ABellil WBen Amar C(2015)Sphere-Tree Semi-regular RemesherProceedings of the 16th International Conference on Advanced Concepts for Intelligent Vision Systems - Volume 938610.1007/978-3-319-25903-1_71(826-837)Online publication date: 26-Oct-2015
https://dl.acm.org/doi/10.1007/978-3-319-25903-1_71
Priorov AProzorov A(2014)Methods of complete surface reconstruction through merging of point clouds according to stereo vision dataProceedings of the 16th Conference of Open Innovations Association FRUCT10.1109/FRUCT.2014.7000930(73-78)Online publication date: 3-Nov-2014
https://dl.acm.org/doi/10.1109/FRUCT.2014.7000930
Dyshkant N(2013)Comparison of point clouds acquired by 3d scannerProceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery10.1007/978-3-642-37067-0_5(47-58)Online publication date: 20-Mar-2013
https://dl.acm.org/doi/10.1007/978-3-642-37067-0_5
Botsch MPauly MKobbelt LAlliez PLévy BBischoff SRössl CMcMains SSloan P(2007)Geometric modeling based on polygonal meshes Video files associated with this course are available from the citation pageACM SIGGRAPH 2007 courses10.1145/1281500.1281640(1-es)Online publication date: 5-Aug-2007
https://dl.acm.org/doi/10.1145/1281500.1281640
Chaine RGandoin PRoudet CLevy BManocha D(2007)Mesh connectivity compression using convection reconstructionProceedings of the 2007 ACM symposium on Solid and physical modeling10.1145/1236246.1236255(41-49)Online publication date: 4-Jun-2007
https://dl.acm.org/doi/10.1145/1236246.1236255
Botsch MPauly MRossl CBischoff SKobbelt LFinnegan JShreiner D(2006)Geometric modeling based on triangle meshesACM SIGGRAPH 2006 Courses10.1145/1185657.1185839(1-es)Online publication date: 30-Jul-2006
https://dl.acm.org/doi/10.1145/1185657.1185839
Mamou KZaharia TPreteux F(2005)A multiple B-Spline representation for progressive 3D mesh compressionProceedings of the 9th WSEAS International Conference on Communications10.5555/1369885.1369956(1-7)Online publication date: 14-Jul-2005
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Peng JKuo C(2005)Geometry-guided progressive lossless 3D mesh coding with octree (OT) decompositionACM SIGGRAPH 2005 Papers10.1145/1186822.1073237(609-616)Online publication date: 31-Jul-2005
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