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Digital and Image Geometry pp 150–162Cite as

Discrete Polyhedrization of a Lattice Point Set

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2243))

Abstract

We introduce a polyhedral representation of surfaces for analysis and recognition of three-dimensional digital images. Our representation is based on combinatorial topology. By using a discrete version of combinatorial topology we also present an algorithm for reconstruction of a polyhedron in a discrete space from a set of lattice points.

The first author has been on leave from School of Information Science, JAIST, Japan, thanks to the JSPS postdoctoral fellowships for research abroad from October 2000.

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References

  1. Rosenfeld, A. (1970): Connectivity in digital pictures. Journal of the Association for Computing Machinery 17 1, 146–160

    MATH  MathSciNet  Google Scholar 

  2. Artzy, E., Frieder, G., Herman, G. T. (1981): The theory, design, implementation, and evaluation of a three-dimensional boundary detection algorithm. Computer Graphics Image Processing 15 1–24

    Article  Google Scholar 

  3. Kong, T. Y., Rosenfeld, A. (1989): Digital topology: introduction and survey. Computer Vision Graphics and Image Processing 48, 357–393

    Article  Google Scholar 

  4. Hausdor, F. (1937): Set theory. Chelsea Publishing Company

    Google Scholar 

  5. Alexandrov, P. S. (1956): Combinatorial topology I. Graylock Press

    Google Scholar 

  6. Stillwell, J. (1993): Classical topology and combinatorial group theory. Springer

    Google Scholar 

  7. Kong, T. Y., Roscoe, A. W., Rosenfeld, A. (1992): Concepts of digital topology. Topology and its Applications 46, 219–262

    Article  MATH  MathSciNet  Google Scholar 

  8. Voss, K. (1993): Discrete images, objects, and functions in Z 3. Springer-Verlag

    Google Scholar 

  9. Tourlakis, G., Mylopoulos, J. (1973): Some results in computational topology. Journal of the Association for Computing Machinery 20 3, 439–455

    MATH  MathSciNet  Google Scholar 

  10. Lorensen, W. E., Cline, H. E. (1987): Marching cubes: a high-resolution 3d surface construction algorithm. Computer Graphics (SIGGRAPH’ 87) 21 4 163–169

    Article  Google Scholar 

  11. Kenmochi, Y., Imiya, A., Ichikawa, A. (1998): Boundary extraction of discrete objects. Computer Vision and Image Understanding 71 3, 281–293

    Article  Google Scholar 

  12. Clifford, W. K. (1956): The postulates of the science of space. The world of mathematics, Simon and Schuster, New York

    Google Scholar 

  13. Kovalevsky, V. A. (1989): Finite topology as applied to image analyses. Computer Vision Graphics and Image Processing 46, 141–161

    Article  Google Scholar 

  14. Morgenthaler, D. G., Rosenfeld, A. (1981): Surfaces in three-dimensional images. Information and Control 51, 227–247

    Article  MATH  MathSciNet  Google Scholar 

  15. Couprie, M., Bertrand, G. (1998): Simplicity surfaces: a new definition of surfaces in Z3. SPIE Vision Geometry VII 3454, 40–51

    Google Scholar 

  16. Françcon, J. (1995): Discrete combinatorial surfaces. CVGIP: Graphical Models and Image Processing 57 1, 20–26

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. ESIEE, Laboratoire A2SI, Cité Descartes, B. P. 99, 93162, Noisy-Le-Grand Cedex, France

    Yukiko Kenmochi

  2. Institute of Media and Information Technology, Chiba University, 1-33 Yayoi-cho Inage-ku, 263-8522, Chiba, Japan

    Atsushi Imiya

Authors
  1. Yukiko Kenmochi
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  2. Atsushi Imiya
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Editor information

Editors and Affiliations

  1. Groupe ESIEE, Cité Descartes, 2, Bld. Blaise-Pascal, 93162, Noisy-le-Grand, France

    Gilles Bertrand

  2. Media Technology Division, Chiba University, Inst. of Media and Information Technology, 1-33 Yayoi-cho, Inage-ku, 263-8522, Chiba, Japan

    Atsushi Imiya

  3. The University of Auckland, CITR Tamaki, Tamaki Campus, Morrin Road, Glen Innes, 1005, Auckland, New Zealand

    Reinhard Klette

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© 2001 Springer-Verlag Berlin Heidelberg

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Kenmochi, Y., Imiya, A. (2001). Discrete Polyhedrization of a Lattice Point Set. In: Bertrand, G., Imiya, A., Klette, R. (eds) Digital and Image Geometry. Lecture Notes in Computer Science, vol 2243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45576-0_9

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  • DOI: https://doi.org/10.1007/3-540-45576-0_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43079-7

  • Online ISBN: 978-3-540-45576-9

  • eBook Packages: Springer Book Archive

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