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Unified Characterization of P-Simple Points in Triangular, Square, and Hexagonal Grids

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Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications (CompIMAGE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10149))

Abstract

Topology preservation is a crucial property of topological algorithms working on binary pictures. Bertrand introduced the notion of P-simple points on the orthogonal grids, which provides a sufficient condition for topology-preserving reductions. This paper presents both formal and easily visualized characterizations of P-simple points in all the three types of regular 2D grids.

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References

  1. Bell, S.B.M., Holroyd, F.C., Mason, D.C.: A digital geometry for hexagonal pixels. Image Vis. Comput. 7, 194–204 (1989)

    Article  Google Scholar 

  2. Bertrand, G.: On \(P\)-simple points. Compte Rendu de l’Académie des Sciences de Paris, Série Math. I(321), 1077–1084 (1995)

    MathSciNet  MATH  Google Scholar 

  3. Bertrand, G., Couprie, M.: Two-dimensional parallel thinning algorithms based on critical kernels. J. Math. Imaging Vis. 31, 35–56 (2008)

    Article  MathSciNet  Google Scholar 

  4. Bertrand, G., Couprie, M.: On parallel thinning algorithms: minimal non-simple Sets, \(P\)-simple points and critical kernels. J. Math. Imaging Vis. 35, 23–35 (2009)

    Article  MathSciNet  Google Scholar 

  5. Brimkov, V.E., Barneva, R.P.: Analytical honeycomb geometry for raster and volume graphics. Comput. J. 48, 180–199 (2005)

    Article  Google Scholar 

  6. Gaspar, F.J., Gracia, J.L., Lisbona, F.J., Rodrigo, C.: On geometric multigrid methods for triangular grids using three-coarsening strategy. Appl. Numer. Math. 59, 1693–1708 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hall, R.W.: Parallel connectivity-preserving thinning algorithms. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological Algorithms for Digital Image Processing, pp. 145–179. Elsevier Science, Amsterdam (1996)

    Chapter  Google Scholar 

  8. Kardos, P., Palágyi, K.: On topology preservation of mixed operators in triangular, square, and hexagonal grids. Discret. Appl. Math., in press. doi:10.1016/j.dam.2015.10.033

  9. Kardos, P., Palágyi, K.: Topology preservation on the triangular grid. Ann. Math. Artif. Intell. 75, 53–68 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kardos, P., Palágyi, K.: On topology preservation in triangular, square, and hexagonal grids. In: Proceedings of the 8th International Symposium on Image and Signal Processing and Analysis, ISPA 2013, pp. 782–787 (2013)

    Google Scholar 

  11. Kardos, P., Palágyi, K.: Topology-preserving hexagonal thinning. Int. J. Comput. Math. 90, 1607–1617 (2013)

    Article  MATH  Google Scholar 

  12. Kardos, P., Palágyi, K.: On topology preservation for triangular thinning algorithms. In: Barneva, R.P., Brimkov, V.E., Aggarwal, J.K. (eds.) IWCIA 2012. LNCS, vol. 7655, pp. 128–142. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34732-0_10

    Chapter  Google Scholar 

  13. Kong, T.Y.: On topology preservation in 2-D and 3-D thinning. Int. J. Pattern Recog. Artif. Intell. 9, 813–844 (1995)

    Article  Google Scholar 

  14. Kong, T.Y., Gau, C.-J.: Minimal non-simple sets in 4-dimensional binary images with (8,80)-adjacency. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 318–333. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30503-3_24

    Chapter  Google Scholar 

  15. Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Comput. Vis. Graph. Image Process. 48, 357–393 (1989)

    Article  Google Scholar 

  16. Marchand-Maillet, S., Sharaiha, Y.M.: Binary Digital Image Processing - A Discrete Approach. Academic Press, Cambridge (2000)

    MATH  Google Scholar 

  17. Middleton, L., Sivaswamy, J.: Hexagonal Image Processing: A Practical Approach. Advances Pattern Recognition. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  18. Nagy, B.: Characterization of digital circles in triangular grid. Pattern Recogn. Lett. 25, 1231–1242 (2004)

    Article  Google Scholar 

  19. Nagy, B., Mir-Mohammad-Sadeghi, H.: Digital disks by weighted distances in the triangular grid. In: Normand, N., Guédon, J., Autrusseau, F. (eds.) DGCI 2016. LNCS, vol. 9647, pp. 385–397. Springer, Heidelberg (2016). doi:10.1007/978-3-319-32360-2_30

    Chapter  Google Scholar 

  20. Ronse, C.: Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images. Discret. Appl. Math. 21, 67–79 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  21. Sarkar, A., Biswas, A., Mondal, S., Dutt, M.: Finding shortest triangular path in a digital object. In: Normand, N., Guédon, J., Autrusseau, F. (eds.) DGCI 2016. LNCS, vol. 9647, pp. 206–218. Springer, Heidelberg (2016). doi:10.1007/978-3-319-32360-2_16

    Chapter  Google Scholar 

  22. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, Cambridge (1982)

    MATH  Google Scholar 

  23. Wuthrich, C., Stucki, P.: An algorithm comparison between square- and hexagonal-based grids. Graph. Models Image Process. 53, 324–339 (1991)

    Article  Google Scholar 

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Acknowledgements

This work was supported by the grant OTKA K112998 of the National Scientific Research Fund.

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Authors and Affiliations

  1. Department of Image Processing and Computer Graphics, University of Szeged, Szeged, Hungary

    Péter Kardos & Kálmán Palágyi

Authors
  1. Péter Kardos
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  2. Kálmán Palágyi
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Correspondence to Kálmán Palágyi .

Editor information

Editors and Affiliations

  1. State University of New York at Fredonia , Fredonia, New York, USA

    Reneta P. Barneva

  2. State University of New York , Buffalo, New York, USA

    Valentin E. Brimkov

  3. Universidade do Porto , Porto, Portugal

    João Manuel R.S. Tavares

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Kardos, P., Palágyi, K. (2017). Unified Characterization of P-Simple Points in Triangular, Square, and Hexagonal Grids. In: Barneva, R., Brimkov, V., Tavares, J. (eds) Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications. CompIMAGE 2016. Lecture Notes in Computer Science(), vol 10149. Springer, Cham. https://doi.org/10.1007/978-3-319-54609-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-54609-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54608-7

  • Online ISBN: 978-3-319-54609-4

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