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From Digital Plane Segmentation to Polyhedral Representation

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Geometry, Morphology, and Computational Imaging

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2616))

Abstract

Many applications, manipulation or just visualization of discrete volumes are time consuming problems. The general idea to solve these difficulties is to transform, in a reversible way, those volumes into Euclidean polyhedra. A first step of this process consists in a Digital Plane Segmentation of the discrete object’s surface. In this paper, we present an algorithm to construct an optimal, in the number of vertices, discrete volume polyhedral representation (i.e. vertices and faces adjacencies).

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References

  1. Ph. Borianne and J. Françon. Reversible polyhedrization of discrete volumes. In DGCI’94, pages 157–168, Grenoble, France, sept. 1994.

    Google Scholar 

  2. L. Buzer. An incremental linear time algorithm for digital line and plane recognition using a linear incremental feasibility problem. In A. Braquelaire, J.-O. Lachaud, and A. Vialard, editors, DGCI’02, volume 2301 of Lect. Notes of Comp. Sci., pages 372–381. Springer Verlag, 2002.

    Google Scholar 

  3. J.M. Chassery, F. Dupont, I. Sivignon, and J. Vittone. Recognition of digital naive planes. In ICIAP’01 11th International Conference on Image Analysis and Processing, pages 662–636, September 2001.

    Google Scholar 

  4. I. Debled-Rennesson and J.-P. Reveillès. An incremental algorithm for digital plane recognition. In DGCI’94, pages 207–222, September 1994.

    Google Scholar 

  5. J. Françon, J. M. Schramm, and M. Tajine. Recognizing arithmetic straight lines and planes. In S. Miguet A. Montanvert and S. Ubéda, editors, DGCI’96, volume 1176 of Lect. Notes of Comp. Sci., pages 141–150. Springer Verlag, 1996.

    Google Scholar 

  6. D. S. Hochbaum, editor. Approximation algorithms for NP-hard problems. PWS Publishing Company, 1997.

    Google Scholar 

  7. C.E. Kim and A. Rosenfeld. Convex digital solids. IEEE Trans. on Pattern Anal. Machine Intell., PAMI-4(6):612–618, 1982.

    Article  MATH  Google Scholar 

  8. C.E. Kim and I. Stojmenović. On the recognition of digital planes in three dimensionnal space. Pattern Recognition Letters, 32:612–618, 1991.

    Google Scholar 

  9. R. Klette. Digital Geometry-The birth of a new discipline, chapter 1. 2001. Retirement of A. Rosenfeld.

    Google Scholar 

  10. R. Klette and H. J. Sun. Digital planar segment based polyhedrization for surface area estimation. In C. Arcelli, L.P. Cordella, and G. Sanniti di Baja, editors, International Workshop on Visual Form 4, volume 2059 of Lect. Notes Comput. Sci., pages 356–366. Springer-Verlag, 2001.

    Google Scholar 

  11. L. Papier and J. Françon. Polyhedrization of the boundary of a voxel object. In M. Couprie G. Bertrand and L. Perroton, editors, DGCI’99, volume 1568 of Lect. Notes of Comp. Sci., pages 425–434. Springer Verlag, 1999.

    Google Scholar 

  12. J.-P. Reveillès. Géométrie discréte, calcul en nombres entiers et algorithmique. PhD thesis, Université Louis Pasteur, 1991.

    Google Scholar 

  13. Carsten Thomassen. On the complexity of finding a minimum cycle cover of a graph. SIAM Journal on Computing, 26(3):675–677, June 1997.

    Article  MATH  MathSciNet  Google Scholar 

  14. P. Veelaert. Digital planarity of rectangular surface segments. IEEE Trans. Pattern Anal. Machine Intell., PAMI-16:647–653, 1994.

    Article  Google Scholar 

  15. P. Veelaert. Concurrency of line segments in uncertain geometry. In A. Braquelaire, J.-O. Lachaud, and A. Vialard, editors, DGCI’02, volume 2301 of Lect. Notes of Comp. Sci., pages 289–300. Springer Verlag, April 2002.

    Google Scholar 

  16. Joëlle Vittone. Caractérisation et reconnaissance de droites et de plans en géométrie discrète. PhD thesis, Université Joseph Fourier, Grenoble, France, 1999.

    Google Scholar 

  17. D. B. West. Introduction to Graph Theory. Prentice Hall, 2 edition, 2001.

    Google Scholar 

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Sivignon, I., Coeurjolly, D. (2003). From Digital Plane Segmentation to Polyhedral Representation. In: Asano, T., Klette, R., Ronse, C. (eds) Geometry, Morphology, and Computational Imaging. Lecture Notes in Computer Science, vol 2616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36586-9_23

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  • DOI: https://doi.org/10.1007/3-540-36586-9_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00916-0

  • Online ISBN: 978-3-540-36586-0

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