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Part of the book series: Computational Imaging and Vision ((CIVI,volume 2))

Abstract

In this paper, we present an algorithm for optimal image segmentation using the Voronoi diagram and the Delaunay graph. The Voronoi diagram is a powerful tool for shape description and image segmentation. The Delaunay graph is used to describe the neighborhood of each Voronoi region. This graph is used to optimize the image segmentation. The validity of our approach is demonstrated by examples.

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References

  • Ahuja, N., An, B. and Schachter, B.: 1992,‘Image representation using Voronoi tessellation’, Computer Vision Graphics and Image processing Vol. 29, pp. 286–295

    Article  Google Scholar 

  • Bertin, E., Parazza, F. and Chassery J.-M.: 1993,‘Segmentation and measurement based on Voronoi diagram: Application to confocal microscopy’, Special issued of Computerized Medical Imaging and Graphics, Vol. 17 no. 3, pp. 175–182

    Article  Google Scholar 

  • Bertin, E.: 1994,‘Diagramme de Voronoï 2D et 3D: Applications en Analyse d’Images’, PhD thesis, Joseph Fourier University, Grenoble, France.

    Google Scholar 

  • Bowyer, A.: 1984,‘Computing Dirichlet tessellation’, The computer journal,Vol. 24 no. 2, pp. 162–166

    Article  MathSciNet  Google Scholar 

  • Brandt, J.W., Algazi, V.R.: 1992,‘Continuous Skeleton Computation by Voronoi Diagram’, Computer Vision Graphics and Image processing Vol. 55, pp. 329–338

    MATH  Google Scholar 

  • Chassery, J.-M. and Melkemi M.: 1991,‘Diagramme de Voronoï appliqué à la segmentation d’images et à la détection d’évéements en imagerie multi-source’Traitement du signal, Vol. 8 no 3, pp. 155–164

    Google Scholar 

  • Geman, S. and Geman, D.: 1984,‘Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images’, IEEE Transaction PAMI,Vol. 6 no 6, pp. 721–741

    Article  MATH  Google Scholar 

  • Marcelpoil, R. and Usson Y.: 1992,‘Methods for the study of cellular sociology: Voronoi diagrams and parametrization of the spatial relationships’, J. Theor Biol, Vol. 154, pp. 359–369

    Article  Google Scholar 

  • Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller A.H. and Teller E.: 1953,‘Equation of the state calculations by fast computing machine’, J. Chem. Phys., Vol. 21, pp. 1087–

    Article  Google Scholar 

  • Okabe, A., Boots B. and Sugihara K.: 1992,‘Spatial Tessellations: Concept and Applications of the Voronoi Diagram’, John Wiley and Sons, New York

    Google Scholar 

  • Preparata J.P. and Shamos M.I.S.: 1988,‘Computational Geometry, an introduction’, Springer Verlag, New York

    Google Scholar 

  • Serra, J. (editor): 1988,‘Image analysis and mathematical morphology, volume 2: theoretical advances’, Academic Press, London

    Google Scholar 

  • Vincent L.: 1991‘Graphs and mathematical morphology’, Signal Processing, Vol. 16 no 4 pp. 365–

    Article  MathSciNet  Google Scholar 

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© 1994 Springer Science+Business Media Dordrecht

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Bertin, E., Marchand-Maillet, S., Chassery, JM. (1994). Optimization in Voronoi Diagrams. In: Serra, J., Soille, P. (eds) Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1040-2_27

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  • DOI: https://doi.org/10.1007/978-94-011-1040-2_27

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4453-0

  • Online ISBN: 978-94-011-1040-2

  • eBook Packages: Springer Book Archive

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