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A Linear Algorithm for Polygonal Representations of Digital Sets

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Combinatorial Image Analysis (IWCIA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4040))

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Abstract

Polygonal representations of digital sets with the same convexity properties allow a simple decomposition of digital boundaries into convex and concave parts.

Representations whose vertices are boundary points, i.e. are integer numbers, attract most attention. The existing linear Algorithm UpPolRep computes polygonal representations with some uncorresponding parts. However, the algorithm is unable to decide if a corresponding polygonal representation still exists and in the case of existence it is unable to compute the representation. Studying situations where uncorrespondences appear we extended the algorithm. The extention does not change the time complexity. If a digital set possesses a corresponding representation then it detects this representation. Otherwise, it recognizes that such representation does not exist.

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References

  1. Debled-Rennesson, I., Reveillès, J.-P.: A linear algorithm for segmentation of digital curves. International Journal of Pattern Recognition and Artificial Intelligence 9, 635–662 (1995)

    Article  Google Scholar 

  2. Debled-Rennesson, I., Rémy, J.-L., Rouyer-Degli, J.: Detection of discrete convexity of polyominoes. Discrete Applied Mathematics 125, 115–133 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dörksen, H.: Shape Representations of Digital Sets based on Convexity Properties. Dissertation. Fachbereich Mathematik. Universität Hamburg (2004), http://www.sub.uni-hamburg.de/opus/volltexte/2005/2332/

  4. Dörksen-Reiter, H., Debled-Rennesson, I.: Convex and Concave Parts of Digital Curves. In: Klette, R., et al. (eds.) Geometric Properties from Incomplete Data, Computational Imaging and Vision, vol. 31. Springer, Heidelberg (2005)

    Google Scholar 

  5. Eckhardt, U., Reiter, H.: Polygonal Representations of Digital Sets. Algorithmica 38(1), 5–23 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Feschet, F., Tougne, L.: Optimal time computation of the tangent of a discrete curve: application to the curvature. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 31–40. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  7. Freeman, H.: On the encoding of arbitrary geometry configurations. IRE Trans. EC 10, 260–268 (1961)

    Article  MathSciNet  Google Scholar 

  8. Klette, R., Rosenfeld, R.: Digital Geometry. Morgan Kaufmann publishers, Elsevier (2004)

    Google Scholar 

  9. Hübler, A.: Diskrete Geometrie für die Digitale Bildverarbeitung. Dissertation B. Friedrich-Schiller-Universität Jena (1989)

    Google Scholar 

  10. Latecki, L., Lakämper, R.: Convexity rule for shape decomposition based on discrete contour evolution. Computer Vision and Image Understanding 73(3), 441–454 (1999)

    Article  Google Scholar 

  11. Reveillès, J.-P.: Géométrie discrète, calcul en nombres entiers et algorithmique. Thése d’État, Strasbourg (1991)

    Google Scholar 

  12. Scherl, W.: Bildanalyse allgemeiner Dokumente. (Informatik-Fachberichte, Band 131). Springer, Heidelberg (1987)

    Google Scholar 

  13. Valentine, F.A.: Convex Sets. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Company, New York (1964)

    MATH  Google Scholar 

  14. Voss, K.: Discrete Images, Objects and Functions in ℤn. Algorithm and Combinatorics, vol. 11. Springer, Heidelberg (1993)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Dörksen-Reiter, H., Debled-Rennesson, I. (2006). A Linear Algorithm for Polygonal Representations of Digital Sets. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds) Combinatorial Image Analysis. IWCIA 2006. Lecture Notes in Computer Science, vol 4040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11774938_24

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  • DOI: https://doi.org/10.1007/11774938_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35153-5

  • Online ISBN: 978-3-540-35154-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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