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Convex Functions on Discrete Sets

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Combinatorial Image Analysis (IWCIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3322))

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Abstract

We propose definitions of digital convex sets and digital convex functions and relate them to a refined definition of digital hyperplanes.

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References

  1. Eckhardt, U.: Digital lines and digital convexity. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 209–228. Springer, Heidelberg (2002)

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  2. Hiriart-Urruty, J.-B., Lemaréchal, C.: Fundamentals of Convex Analysis X + 259 p. Springer, Heidelberg (2001)

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  3. Hörmander, L.: Notions of Convexity, viii + 414 p. Birkhäuser, Boston (1994)

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  4. Melin, E.: Digital straight lines in the Khalimsky plane, Department of Mathematics, Report 2003:30. Uppsala University. Accepted for publication in Mathematica Scandinavica (2003)

    Google Scholar 

  5. Reveillés, J.-P.: Géométrie discréte, calcul en nombres entiers et algorithmique, p. 251. Université Louis Pasteur, Strasbourg, Thèse d’État (1991)

    Google Scholar 

  6. Rosenfeld, A.: Digital straight line segments. IEEE Transactions on Computers c-32(12), 1264–1269 (1974)

    Article  MathSciNet  Google Scholar 

  7. Rosenfeld, A., Klette, R.: Digital straightness. Electronic Notes in Theoretical Computer Science 46, 32 (2001), http://www.elsevier.nl/locate/entcs/volume46.html

    Article  Google Scholar 

  8. Singer, I.: Abstract Convex Analysis, xix + 491 p. John Wiley & Sons, Inc., Chichester (1997)

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© 2004 Springer-Verlag Berlin Heidelberg

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Kiselman, C.O. (2004). Convex Functions on Discrete Sets. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_32

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  • DOI: https://doi.org/10.1007/978-3-540-30503-3_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23942-0

  • Online ISBN: 978-3-540-30503-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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