Cluster Computing

, Volume 22, Supplement 6, pp 14253–14267 | Cite as

Novel algorithm for generating basis convex hexagonal polygons and polyhedrons

  • Mohd. Sherfuddin KhanEmail author
  • E. G. Rajan
  • Vijay H. Mankar


Geometric Filters (G-Filters) are efficient shape filters than morphological filters. In this paper, the Algorithms for constructing basis hexagonal polygons and polyhedrons are developed. The development process involves 2 Algorithms. The 1st Algorithm describes process of constructing 18 convex polygons and 324 convex polyhedrons. The 2nd one describes way of constructing the 5 Basis convex hexagonal polygons and 25 basis convex polyhedrons. This polygons and polyhedrons are used as masks for processing 2D or 3D hexagonal images captured with hexagonal camera or hexagonalized images which are captured by using rectangular camera. Instead of using this 18 polygons and 324 polyhedrons one can use this 5 basis polygons and 25 basis polyhedrons for processing.


Geometric filters Convex polygons Polyhedrons 3D hexagonal lattice 



The Authors are thankful to G. Chitra MD of Pentagram Research Center Pvt Ltd Hyderabad for allowing to do research and providing the infrastructure, technical and programming team and a heartful thanks to my prof Dr. E. G Rajan sir for his continues guidance and support.


  1. 1.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Pearson Education, Inc., (2004)Google Scholar
  2. 2.
    Rajan, E.G.: Symbolic Computing-Signal and Image Processing. BS Publications, Hyderabad (2003)Google Scholar
  3. 3.
    Choquet, G.: Topology. Academic, New York (1966)zbMATHGoogle Scholar
  4. 4.
    Rajan, E.G.: The notion of geometric filters and their use in computer vision. In: 1995 IEEE International Conference on Systems, Man and Cybernetics, Vancouver, B.C., Canada, pp. 4250–4255 (1995)Google Scholar
  5. 5.
    Rajan, E.G.: On the notion of a geometric filter and its relevance in the neighbourhood processing of digital images in hexagonal grids. In: 4th International Conference on Control, Automation, Robotics and Vision, Westim Stamford, Singapore (1996)Google Scholar
  6. 6.
    Vasantha, N., Rajan, E.G.: On the notion of geometric filters. In: National Conference Organized by the Institution of Engineers, India and Annamalai University, SURGE’94 (1994)Google Scholar
  7. 7.
    Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)zbMATHGoogle Scholar
  8. 8.
    Serra, J.: Image Analysis and Mathematical Morphology. Acadamic, New York (1982)zbMATHGoogle Scholar
  9. 9.
    Maragos, P., Scharer, R.W.: Applications of morphological filtering to image processings and analysis. In: Proceedings of 1986 IEEE International Conference on Acoustics, Speech, and Signal Processing, Tokyo, Japan, pp. 2067–2070 (1986)Google Scholar
  10. 10.
    Sonka, M., Hlavac, V., Boyele, R.: Image Processing, Analysis, and Machine Vision, 3rd edn. Brooks Cole (2008)Google Scholar
  11. 11.
    Sultana, T., Rajan, E.G.: Algebra of Geometric Filters Defined Over Three Dimensional Rectangular Lattice—Part I, Paper submitted to this conference along with this paperGoogle Scholar
  12. 12.
    Senthilnayaki, M., Veni, S., Kutty, K.N.: Hexagonal pixel grid modeling for edge detection and design of cellular architecture for binary image skeletonization. In: IEEE Annual Conference on India, pp. 1–6 (2006)Google Scholar
  13. 13.
    Narayanankutty, K.A.: Image enhancement of medical images using Gabor Filter Bank on hexagonal sampled grids. Int. J. Electr. Comput. Energ. Electron. Commun. Eng. 4(5), 853–858 (2010)Google Scholar
  14. 14.
    Elvins, T.T.: A survey of algorithms for volume visualization. ACM Siggraph Comput. Gr. 26(3), 194–201 (1992)CrossRefGoogle Scholar
  15. 15.
    Snyder, W.E., Qi, H., Sander, W.: A coordinate system for hexagonal pixels. In: Proceedings of SPIE, pp. 716–727 (1999)Google Scholar
  16. 16.
    Lee, M., Jayanthi, S.: Hexagonal Image Processing: A Practical Approach (Advances in Pattern Recognition). Springer, NewYork (2005)zbMATHGoogle Scholar
  17. 17.
    Marchand-Maillet, S., Sharaiha, Y.M.: Binary Digital Image Processing—A Discrete Approach. Academic Press, NewYork (2000)zbMATHGoogle Scholar
  18. 18.
    Hartman, N.P., Tanimoto, S.L.: A Hexagonal Pyramid Data Structure for Image Processing. In: IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-14, pp. 247–256 (1984)CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research CenterG.H Raisoni College of EngineeringNagpurIndia
  2. 2.Pentagram Research CentreHyderabadIndia
  3. 3.Government PolytechnicAhmednagarIndia

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