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3D modelling and segmentation with discrete curvatures

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recent concepts of discrete curvatures are very important for Medical and Computer Aided Geometric Design applications. A first reason is the opportunity to handle a discretisation of a continuous object, with a free choice of the discretisation. A second and most important reason is the possibility to define second-order estimators for discrete objects in order to estimate local shapes and manipulate discrete objects. There is an increasing need to handle polyhedral objects and clouds of points for which only a discrete approach makes sense. These sets of points, once structured (in general meshed with simplexes for surfaces or volumes), can be analysed using these second-order estimators. After a general presentation of the problem, a first approach based on angular defect, is studied. Then, a local approximation approach (mostly by quadrics) is presented. Different possible applications of these techniques are suggested, including the analysis of 2D or 3D images, decimation, segmentation... We finally emphasise different artefacts encountered in the discrete case.
Rocznik
Tom
Strony
13--24
Opis fizyczny
Bibliogr. 34 poz., rys.
Twórcy
autor
  • LSIS Laboratory, University of Marseille. ESIL, Campus de Luminy, case 925, 13288 Marseille Cedex 9, France
autor
  • LSIS Laboratory, University of Marseille. ESIL, Campus de Luminy, case 925, 13288 Marseille Cedex 9, France
  • LSIS Laboratory, University of Marseille. ESIL, Campus de Luminy, case 925, 13288 Marseille Cedex 9, France
Bibliografia
  • [1] AICHHOLZER O., ALBOUL L. and HURTADO F.: On flips in polyhedral surfaces. International Journal of Foundations of Computer Science, vol. 13(2), pp. 303-311, 2002.
  • [2] ALBOUL L. and VAN DAMME R.: Polyhedral metrics in surface reconstruction: tight triangulations. Memorandum n. 1275, Twente University, Holland, 1995.
  • [3] ALBOUL L. and VAN DAMME R.: Tight triangulations. Mathematical Methods for Curves and Surfaces, pp. 517-526, 1995.
  • [4] ALBOUL L., KLOOSTERMAN G., TRAAS C. and VAN DAMME R.: Best data-dependent triangulations. Journal of computational and applied mathematics, vol. 119, pp. 1-12, 2000.
  • [5] ALBOUL L.: Optimising triangulated polyhedral surfaces with self-intersections. 10th IMA Conference (Mathematics of Surfaces), LNCS 2768, Springer Verlag, pp. 48-72, 2003.
  • [6] ALEXANDROV A.: Intrinsic geometry of surfaces. Transactions of mathematical monographs AMS 1967.
  • [7] BAHI A., BOUAKAZ S. and VANDORPE D.: Differential properties of surfaces from unorganized points. ACCV'95 Second Asian Conference on Computer Vision, pp. 37-41, Singapore, 1995.
  • [8] BLOOR M. and WILSON M.: Using partial differential equations to generate free-form surface design. Computer-Aided design, vol. 22, pp. 202-212, 1990.
  • [9] BOIX E.: Approximation linéaire des surfaces de R3 et applications. PHD Thesis, Ecole Polytechnique, France, 1995.
  • [10] BORRELLI V.: Courbures discrètes. DEA, Université Claude Bernard, France, 1993.
  • [11] BORRELLI V., CAZALS F. and MORVAN J.-M.: On the angular defect of triangulations and the pointwise approximation of curvatures. Computer Aided Geometric Design, vol. 20, pp. 319-341, 2003.
  • [12] BOUSQUET J.: Détection et élimination d'irrégularités sur les surfaces manipulées en CAO. PHD Thesis, Université de Nantes, France, 1997.
  • [13] BOUSQUET J. and DANIEL M.: Flaw removal on Surfaces. Curves and Surfaces with Application in CAGD, Vanderbilt University Press, A. Le Mehauté, C. Rabut and L.L. Schumaker edt, pp. 43-52, 1997.
  • [14] CAZALS F. and POUGET M.: Estimating differential quantities using polynomial fitting of osculating jets. Computer Aided Geometric Design, vol. 22, pp. 121-146, 2005.
  • [15] CHEEGER J., MULLER W. and SCHRADER R.: On the curvature of piecewise flat spaces. Communication in Mathematical Physics, vol. 92, pp. 405-454, 1984.
  • [16] DARBOUX G.: Leçons sur la théorie générale des surfaces. Gabay, Paris 1993, initial text: 1894.
  • [17] DO CARMO M.: Differential geometry of curves and surfaces. Prentice-Hall, 1976.
  • [18] DOUROS I. and BUXTON B.F.: Three-dimensional surface curvature estimation using quadric surface. Scanning 2002 proceedings, May 2002.
  • [19] DYN N., HORMANN K., KIM S-J. and LEVIN D.: Optimizing 3D triangulations using discrete curvature analysis. Mathematical methods in CAGD, Vanderbilt University Press, T. Lyche, L.L. Schumaker edt., pp. 135-146, 2000.
  • [20] FU J.H.G.: Convergence of curvatures in secant approximations. Journal of Differential Geometry, vol. 37, pp. 177-190, 1993.
  • [21] KOBBELT L.: Discrete fairing. Proceedings of 7th IMA Conference on Mathematics of Surfaces, pp. 101-131, 1997.
  • [22] KOBBELT L., CAMPAGNA S. and SEIDEL H.-P.: A general framework for mesh decimation. Proceedings of Graphics Interface Conference, pp.43-50, 1998.
  • [23] KOBBELT L., CAMPAGNA S., VORSATZ S. and SEIDEL H.-P.: Interactive Multi-resolution modeling on arbitrary meshes. SIGGRAPH'98 Conference Proceedings, pp. 105-114, 1998.
  • [24] KRESK P., LUKACS G. and MARTIN R.R.: Algorithms for Computing Curvatures from Range Data. The Mathematics of surfaces 8, Birmingham, UK, IMA Conference, 1998.
  • [25] MEEK D.S. and WALTON D.J.: On surface normal and Gaussian curvature approximations given data sampled from a smooth surface. Computer-Aided Geometric Design, vol. 17, pp. 521-543, 2000.
  • [26] MEYER M., DESBRUN M., SCHRODER P., BARR A.: Discrete differential-geometry operators for triangulated 2-manifolds. Proceedings of VISMATH 2002, 2002.
  • [27] SANDER P. and ZUCKER S.: Inferring surface trace and differential structure from 3D images. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12 (9), pp. 833-854, 1990.
  • [28] SCHNEIDER R. and KOBBELT L.: Geometric fairing of irregular meshes for free-form surface design. Computer-Aided Geometric Design, vol. 18(4), pp. 359-379, 2001.
  • [29] SURAZHSKY T., MAGID E., SOLDEA O., ELBER G. and RIVLIN R.,:A comparison of Gaussian and mean curvatures estimation methods on triangular meshes. IEEE International Conference on Robotics & Automation, 2003.
  • [30] TAUBIN G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. ICCV, pp. 902-907, 1995.
  • [31] TRAUTMANN A.: Comparaison d'indicateurs de courbures discrètes. DEA, Université Aix-Marseille II, 2003.
  • [32] VÉRON P.: Techniques de simplification de modèles polyhédriques pour un environnement de conception mécanique. PHD Thesis, Institut National Polytechnique de Grenoble, France, 1997.
  • [33] VÉRON P., LESAGE D. and LÉON J.-C.: Outils de base pour l'extraction de caractéristiques de surfaces numérisées. Revue internationale de CFAO et d'Informatique Graphique, vol. 13(4, 5, 6), 1998.
  • [34] WATANABE K. and BELYAEV A.G.: Detection of salient curvature features on polygonal surfaces. EUROGRAPHICS, 2001.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0012-0001
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