We present two applications of discrete curvatures for surface mesh processing. The first one deals withÊsimplifying a mesh while preserving its sharp features. The second application can be considered as a dual problem, as we investigate ways to detect feature lines within a mesh. Both applications are illustrated with valuable results.
DOI: 10.5802/acirm.53
@article{ACIRM_2013__3_1_31_0,
author = {Alexandra Bac and Jean-Luc Mari and Dimitri Kudelski and Nam-Van Tran and Sophie Viseur and Marc Daniel},
title = {Application of discrete curvatures to surface mesh simplification and feature line extraction},
journal = {Actes des rencontres du CIRM},
pages = {31--49},
publisher = {CIRM},
volume = {3},
number = {1},
year = {2013},
doi = {10.5802/acirm.53},
zbl = {1434.65018},
language = {en},
url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.53/}
}
TY - JOUR AU - Alexandra Bac AU - Jean-Luc Mari AU - Dimitri Kudelski AU - Nam-Van Tran AU - Sophie Viseur AU - Marc Daniel TI - Application of discrete curvatures to surface mesh simplification and feature line extraction JO - Actes des rencontres du CIRM PY - 2013 SP - 31 EP - 49 VL - 3 IS - 1 PB - CIRM UR - https://acirm.centre-mersenne.org/articles/10.5802/acirm.53/ DO - 10.5802/acirm.53 LA - en ID - ACIRM_2013__3_1_31_0 ER -
%0 Journal Article %A Alexandra Bac %A Jean-Luc Mari %A Dimitri Kudelski %A Nam-Van Tran %A Sophie Viseur %A Marc Daniel %T Application of discrete curvatures to surface mesh simplification and feature line extraction %J Actes des rencontres du CIRM %D 2013 %P 31-49 %V 3 %N 1 %I CIRM %U https://acirm.centre-mersenne.org/articles/10.5802/acirm.53/ %R 10.5802/acirm.53 %G en %F ACIRM_2013__3_1_31_0
Alexandra Bac; Jean-Luc Mari; Dimitri Kudelski; Nam-Van Tran; Sophie Viseur; Marc Daniel. Application of discrete curvatures to surface mesh simplification and feature line extraction. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 31-49. doi : 10.5802/acirm.53. https://acirm.centre-mersenne.org/articles/10.5802/acirm.53/
[1] 3D modeling and segmentation with discrete curvatures, Medical Informatics and Technology (2005), pp. 13-24
[2] Intrinsic geometry of surfaces, Transactions of mathematical monograph AMS (1967)
[3] Skeleton Extraction by Mesh Contraction, ACM Transaction on Graphics, Volume 27 (2008) no. 3, pp. 1-10
[4] Traitement de surfaces géologiques pour la construction de modèles 3D, journées du GTMG (2005), pp. 22-23
[5] Simple points, topological numbers and geodesic neighborhoods in cubic grids, Patterns Recognition Letters, Volume 15 (1994), pp. pp. 1003-1011 | DOI
[6] A Boolean characterization of three-dimensional simple points, Pattern Recognition Letters, Volume 17 (1996), pp. 115-124 | DOI
[7] Model Simplification In Reverse, Vector Quantization, University of Alberta (2000) (Ph. D. Thesis)
[8] Estimating differential quantities using polynomial fitting of osculating jets, Comput. Aided Geom. Des., Volume 22 (2005) no. 2, pp. 121-146 | DOI | MR | Zbl
[9] Motion capture using joint skeleton tracking and surface estimation, IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’09) (2009), pp. 1746-1753
[10] Quadric-Based Polygonal Surface Simplification, Carnegie Mellon University (1999) (Ph. D. Thesis)
[11] A multiphase approach to efficient surface simplification, VIS ’02: Proceedings of the conference on Visualization ’02 (2002), pp. 117-124
[12] A novel cubic-order algorithm for approximating principal direction vectors, ACM Transaction on Graphics, Volume 23 (2004) no. 1, pp. 45-63 | DOI
[13] Principal component analysis, Springer Verlag, 1986 | DOI | Zbl
[14] 3D Feature Line Detection Based on Vertex Labeling and 2D Skeletonization, IEEE International Conference on Shape Modeling and Applications (SMI’10) (2010), pp. 246-250
[15] Extraction of feature lines with connectivity preservation, Computer Graphics International (CGI’11 electronic proceedings) (2011)
[16] Building skeleton models via 3-D medial surface/axis thinning algorithms, Graphical Models and Image Processing, Volume 56 (1994) no. 6, pp. 462-478 | DOI
[17] Out-of-core simplification of large polygonal models, SIGGRAPH ’00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques (2000), pp. 259-262 | DOI
[18] Surface sketching with a voxel-based skeleton, 15th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI’09) (Lecture Notes in Computer Science), Volume 5810, Springer, 2009, pp. 325-336 | DOI | Zbl
[19] Discrete Differential Geometry Operators for Triangulated 2-Manifolds, VisMath (2002) citeseer.ist.psu.edu/meyer02discrete.html
[20] Multi-resolution 3D approximation for rendering complexe scences, Geometric Modeling In Computer Graphics (1993), pp. 455-465 | DOI
[21] Extraction of feature lines on triangulated surfaces using morphological operators, AAAI Spring Symposium on Smart Graphics, Volume 00-04 (2000), pp. 71-75
[22] Efficient adaptative simplification of massive meshes, In Proceedings of IEEE Visualization 2001 (2001), pp. 127-134 | DOI
[23] Medial Representations. Mathematics, Algorithms and Applications, Computational Imaging and Vision, Vol. 37, Springer, 2008 | Zbl
[24] Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation, Fifth International Conference on Computer Vision (1995), pp. 902-907 | DOI
[25] Numerical Recipe in C/C++, The Art of Scientific Computing, 2003
[26] Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces, Comput. Aided Geom. Des., Volume 23 (2006) no. 2, pp. 193-207 | DOI | MR | Zbl
[27] Skeleton-Based Recognition of Chinese Calligraphic Character Image, Advances in Multimedia Information Processing (PCM’08) (Lecture Notes in Computer Science), Volume 5353, Springer, 2008, pp. 228-237
[28] A Fast Parallel Algorithm for Thinning Digital Patterns, Communications of the ACM, Volume 27 (1984) no. 3, pp. 236-239 | DOI
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