Table of Contents
ISRN Discrete Mathematics
Volume 2014, Article ID 436419, 6 pages
http://dx.doi.org/10.1155/2014/436419
Research Article

Mathematical Morphology on Hypergraphs Using Vertex-Hyperedge Correspondence

1Department of Computer Applications, Cochin University of Science and Technology, Cochin 682022, India
2Naval Physical and Oceanographic Laboratory, Cochin 682021, India
3Department of Mathematics, Rajagiri School of Engineering and Technology, Cochin 682039, India

Received 18 December 2013; Accepted 27 January 2014; Published 13 March 2014

Academic Editors: A. V. Kelarev, W. F. Klostermeyer, and X. Meng

Copyright © 2014 Bino Sebastian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. C. Gonzalez and E. Richard, Woods, Digital Image Processing, Prentice Hall Press, 2002.
  2. J. P. Serra, Image Analysis and Mathematical Morphology, 1982.
  3. M. Jourlin, B. Laget, G. Matheron et al., Image Analysis and Mathematical Morphology. Vol. 2: Theoretical Advances, 1988. View at MathSciNet
  4. F. Y. Shih, Image Processing and Mathematical Morphology: Fundamentals and Applications, CRC Press, Boca Raton, Fla, USA, 2010. View at MathSciNet
  5. H. J. A. M. Heijmans and C. Ronse, “The algebraic basis of mathematical morphology. I: dilations and erosions,” Computer Vision, Graphics, and Image Processing, vol. 50, no. 3, pp. 245–295, 1990. View at Google Scholar
  6. C. Ronse, “Why mathematical morphology needs complete lattices,” Signal Processing, vol. 21, no. 2, pp. 129–154, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Cousty, L. Najman, F. Dias, and J. Serra, “Morphological filtering on graphs,” Computer Vision and Image Understanding, vol. 117, no. 4, pp. 370–385, 2013. View at Google Scholar
  8. J. Cousty, L. Najman, and J. Serra, “Some morphological operators in graph spaces,” in Mathematical Morphology and Its Application to Signal and Image Processing, vol. 5720, pp. 149–160, Springer, Berlin, Germay, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Heijmans and L. Vincent, “Graph morphology in image analysis,” in Mathematical Morphology in Image Processing, vol. 34, pp. 171–203, Dekker, 1993. View at Google Scholar · View at MathSciNet
  10. L. Vincent, “Graphs and mathematical morphology,” Signal Processing, vol. 16, no. 4, pp. 365–388, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  11. F. Dias, J. Cousty, and L. Najman, “Some morphological operators on simplicial complex spaces,” in Discrete Geometry for Computer Imagery, vol. 6607, pp. 441–452, Springer, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. I. Bloch and A. Bretto, “Mathematical morphology on hypergraphs: preliminary definitions and results,” in Discrete Geometry for Computer Imagery, vol. 6607, pp. 429–440, Springer, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. I. Bloch and A. Bretto, “Mathematical morphology on hypergraphsapplication to similarity and positive kernel,” Computer Vision and Image Understanding, vol. 117, no. 4, pp. 342–354, 2013. View at Google Scholar
  14. I. Bloch, A. Bretto, and A. Leborgne, “Similarity between hypergraphs based on mathematical morphology,” in Mathematical Morphology and Its Applications to Signal and Image Processing, pp. 1–12, Springer, 2013. View at Google Scholar
  15. J. G. Stell, “Relations on hypergraphs,” in Relational and Algebraic Methods in Computer Science, vol. 7560, pp. 326–341, Springer, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. L. Najman and F. Meyer, “A short tour of mathematical morphology on edge and vertex weighted graphs,” in Image Processing and Analysis With Graphs: Theory and Practice, pp. 141–174, 2012. View at Google Scholar
  17. A. Bretto, J. Azema, H. Cherifi, and B. Laget, “Combinatorics and image processing,” Graphical Models and Image Processing, vol. 59, no. 5, pp. 265–277, 1997. View at Google Scholar
  18. C. Berge, Hypergraphs: Combinatorics of Finite Sets, vol. 45, North-Holland Publishing, Amsterdam, The Netherlands, 1989. View at MathSciNet
  19. H. J. A. M. Heijmans, “Composing morphological filters,” IEEE Transactions on Image Processing, vol. 6, no. 5, pp. 713–723, 1997. View at Google Scholar