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Education forum: digital geometry and its algorithms: an introduction

Published:03 June 2013Publication History
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Abstract

This paper gives a brief introduction to digital geometry and its relationships to algorithm analysis, image processing, and computer graphics. Digital geometry highly relates to graph theory, discrete geometry, and computational geometry. We also suggest that digital geometry can be taught as a chapter in computational geometry or geometric methods for computing sciences courses.

References

  1. L. Chen, Discrete Surfaces and Manifolds, Sp Computing, Rockville, 2004.Google ScholarGoogle Scholar
  2. L. Chen, Determining the Number of Holes of a 2D Digital Component is Easy, http://arxiv.org/abs/1211.3812.Google ScholarGoogle Scholar
  3. L. Chen, and Y. Rong, Digital topological method for computing genus and the Betti numbers, Topology and its Applications, Vol 157, No. 12, 2010, 1931--1936.Google ScholarGoogle ScholarCross RefCross Ref
  4. T.K. Dey, S. Guha, Computing Homology Groups Of Simplicial Complexes In R3. Journal Of The ACM 45 (1998) 266--287. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. D.Z. Du, D.J. Kleitman, Diameter and radius in the Manhattan metric, Discrete Comput. Geometry 5 (1990), 351--356.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. R. Klette, and A. Rosenfeld Digital Geometry: Geometric Methods Digital Image Analysis. Morgan Kaufmann, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. J. Shi and J. Malik. Normalized cuts and image segmentation. IEEE Trans. on PAMI, 22(8):888--905, Aug. 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. J. Tenenbaum, V. de Silva, and J. Langford, A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science, vol. 290, pp. 2319--2323, Dec. 2000.Google ScholarGoogle ScholarCross RefCross Ref

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        • Published in

          cover image ACM SIGACT News
          ACM SIGACT News  Volume 44, Issue 2
          June 2013
          142 pages
          ISSN:0163-5700
          DOI:10.1145/2491533
          Issue’s Table of Contents

          Copyright © 2013 Author

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 3 June 2013

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