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International Conference on Computer Vision and Graphics

ICCVG 2010: Computer Vision and Graphics pp 411–419Cite as

Shape Representation and Shape Coefficients via Method of Hurwitz-Radon Matrices

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6374))

Abstract

Computer vision needs suitable methods of shape representation and contour reconstruction. One of them called method of Hurwitz-Radon Matrices (MHR) can be used in representation and reconstruction of shapes of the objects in the plane. Another problem is connected with shape coefficients. This paper contains the way of length estimation and area estimation via MHR method. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. The shape is represented by the set of nodes. It is shown how to create the orthogonal and discrete OHR and how to use it in a process of shape representation and reconstruction. MHR method is interpolating the curve point by point without using any formula or function.

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References

  1. Ballard, D.H.: Computer Vision. Prentice Hall, New York (1982)

    Google Scholar 

  2. Tadeusiewicz, R., Flasiński, M.: Image Recognition. PWN, Warsaw (1991)

    Google Scholar 

  3. Chora”s, R.S.: Computer Vision. Exit, Warsaw (2005)

    Google Scholar 

  4. Jakóbczak, D., Kosiński, W.: Application of Hurwitz - Radon Matrices in Monochromatic Medical Images Decompression. In: Kowalczuk, Z., Wiszniewski, B. (eds.) Intelligent Data Mining in Diagnostic Purposes: Automatics and Informatics, pp. 389–398. PWNT, Gdansk (2007)

    Google Scholar 

  5. Latecki, L.J., Lakaemper, R.: Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution. Computer Vision and Image Understanding 3(73), 441–454 (1999)

    Article  Google Scholar 

  6. Cierniak, R.: Computed Tomography. Exit, Warsaw (2005)

    Google Scholar 

  7. Soussen, C., Mohammad-Djafari, A.: Polygonal and Polyhedral Contour Reconstruction in Computed Tomography. IEEE Transactions on Image Processing 11(13), 1507–1523 (2004)

    Article  MathSciNet  Google Scholar 

  8. Tang, K.: Geometric Optimization Algorithms in Manufacturing. Computer – Aided Design & Applications 2(6), 747–757 (2005)

    Google Scholar 

  9. Kozera, R.: Curve Modeling via Interpolation Based on Multidimensional Reduced Data. Silesian University of Technology Press, Gliwice (2004)

    Google Scholar 

  10. Dahlquist, G., Bjoerck, A.: Numerical Methods. Prentice Hall, New York (1974)

    Google Scholar 

  11. Ralston, A.: A First Course in Numerical Analysis. McGraw-Hill Book Company, New York (1965)

    MATH  Google Scholar 

  12. Eckmann, B.: Topology, Algebra, Analysis- Relations and Missing Links. Notices of the American Mathematical Society 5(46), 520–527 (1999)

    MathSciNet  Google Scholar 

  13. Citko, W., Jakóbczak, D., Sieńko, W.: On Hurwitz - Radon Matrices Based Signal Processing. In: Workshop Signal Processing at Poznan University of Technology (2005)

    Google Scholar 

  14. Tarokh, V., Jafarkhani, H., Calderbank, R.: Space-Time Block Codes from Orthogonal Designs. IEEE Transactions on Information Theory 5(45), 1456–1467 (1999)

    Article  MathSciNet  Google Scholar 

  15. Sieńko, W., Citko, W., Wilamowski, B.: Hamiltonian Neural Nets as a Universal Signal Processor. In: 28th Annual Conference of the IEEE Industrial Electronics Society IECON (2002)

    Google Scholar 

  16. Sieńko, W., Citko, W.: Hamiltonian Neural Net Based Signal Processing. In: The International Conference on Signal and Electronic System ICSES (2002)

    Google Scholar 

  17. Jakóbczak, D.: 2D and 3D Image Modeling Using Hurwitz-Radon Matrices. Polish Journal of Environmental Studies 4A(16), 104–107 (2007)

    Google Scholar 

  18. Tadeusiewicz, R., Korohoda, P.: Computer Analysis and Image Processing. FPT, Cracow (1997)

    Google Scholar 

  19. Jakóbczak, D.: Curve Interpolation Using Hurwitz-Radon Matrices. Polish Journal of Environmental Studies 3B(18), 126–130 (2009)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electronics and Computer Science, Technical University of Koszalin, Śniadeckich 2, 75-453, Koszalin, Poland

    Dariusz Jakóbczak

Authors
  1. Dariusz Jakóbczak
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Editor information

Editors and Affiliations

  1. Polish-Japanese Institute of Information Technology, 86 Koszykowa St, 02-008, Warsaw, Poland

    Leonard Bolc

  2. Institute of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Faculty of Applied Informatics and Mathematics, Department of Informatics, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776, Warsaw, Poland

    Leszek J. Chmielewski

  4. Polish-Japanese Institute of Information Technology, 86 Koszykowa St, 02-008 Warsaw, konradw@pjwstk.edu.pl, The Silesian University of Technology, Institute of Computer Science, Akademicka 16, 44-100 Gliwice, Polan

    Konrad Wojciechowski

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© 2010 Springer-Verlag Berlin Heidelberg

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Jakóbczak, D. (2010). Shape Representation and Shape Coefficients via Method of Hurwitz-Radon Matrices. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds) Computer Vision and Graphics. ICCVG 2010. Lecture Notes in Computer Science, vol 6374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15910-7_47

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  • DOI: https://doi.org/10.1007/978-3-642-15910-7_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15909-1

  • Online ISBN: 978-3-642-15910-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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