Farey Sequence for Error Correcting Codes and Medical Images

  • Authors

    • M Poornima
    • S Jagannathan
    • R Chandrasekhar
    • S T Kumara
    2018-08-04
    https://doi.org/10.14419/ijet.v7i3.1.16812
  • Error correcting codes, image coding, reduced arithmetic floating point, fixed point, digital signal processing and farey sequences.

  • A new scheme for Error Correcting Codes and the coding of medical images through Farey Sequence is brought in the paper. It brings out the reduced real point representations and more of integer point representations. The test case and outcomes are explained in the section 4 and 5.

     

     

  • References

    1. [1] R. Graham etc., Addison-Wesley, 1994. 2. C. E. Patrascu and M.Patrascu. Computing Order Statistics in the Farey Sequence, issue ANTS 2004: 358-366.

      [2] J. Pawlewicz, Order statistics in the Farey sequences in sublinear time and counting primitive lattice points in polygons. Algorithmica 55(2): 271-282, 2009.

      [3] S. Das, K. Halder, S. Pratihar, and P. Bhowmick, Properties of Farey Sequence and their Applications to Digital Image
      Processing, 4th Intl. Conf. on Information Processing, 6-8 August, Bangalore University, Bangalore, pp. 71-81, 2010,
      (IK International Publishing House Pvt. Ltd. New Delhi, 2010, ISBN 978-93-80578-46-0).

      [4] Jonathan Ainsworth, etc., The Farey Sequence , School of Mathematics, University of Edinburgh, March 15, 2012.

      [5] G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. OxfordUniversity Press, New York, 1968.

      [6] E. H. Neville. The Farey Series of Order 1025. Cambridge University Press, 1950.

      [7] P. L. Rosin. Techniques for assessing polygonal approximation of curves. IEEE Trans.PAMI, 19(6): 659-666, 1997.

      [8] M. Schroeder. Fractions: Continued, Egyptian and Farey (Chapter 5). Number Theory inSc. & Communication, vol. 7, Springer Series in Information Sciences, 2006.

      [9] C.-H. Teh and R. T. Chin. On the detection of dominant points on digital curves. IEEE Trans. PAMI, 2(8):859-872, 1989.

      [10] P. Y. Yin. Ant colony search algorithms for optimal polygonal approximation of planecurves. Pattern Recognition, 36:1783-1797, 2003.

      [11] K. Wall and P.-E. Danielsson, A fast sequential method for polygonal approximation of digitized curves, Computer Vision, Graphics, and Image Processing, 28:220-227, 1984.

      [12] Narkhede H P , Review of Image Segmentation Techniques, International Journal of Science and Modern Engineering (IJISME) ISSN: 2319-6386, Volume-1, Issue-8, July 2013 54.

      [13] Digital Image Processing, Rafael C. Gonzalez & Richard E. Woods, Second Edition 2002, Prentice Hall.

      [14] K. K Singh, A Singh,“A Study of Image Segmentation Algorithms for Different Types of Imagesâ€, International Journal of Computer Science Issues, Vol. 7, Issue 5, 2010.

      [15] Chunming Li, Rui Huang, Zhaohua Ding, J. Chris Gatenby, Dimitris N. Metaxas, A Level Set Method for Image Segmentation, in the Presence of Intensity nhomogeneities, With Application to MRI, IEEE Transactions on Image processing, Vol. 20, NO. 7, July 2011.

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  • How to Cite

    Poornima, M., Jagannathan, S., Chandrasekhar, R., & T Kumara, S. (2018). Farey Sequence for Error Correcting Codes and Medical Images. International Journal of Engineering & Technology, 7(3.1), 118-120. https://doi.org/10.14419/ijet.v7i3.1.16812