Shape Parametrization and Contour Curvature Using Method of Hurwitz-Radon Matrices

  • Dariusz Jakóbczak
  • Witold Kosiński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7267)

Abstract

A method of Hurwitz-Radon Matrices (MHR) is proposed to be used in parametrization and interpolation of contours in the plane. Suitable parametrization leads to curvature calculations. Points with local maximum curvature are treated as feature points in object recognition and image analysis. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. It is shown how to create the orthogonal OHR and how to use it in a process of contour parametrization and curvature calculation.

Keywords

Object Recognition Curve Point Contour Point Curvature Calculation Successive Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ballard, D.H.: Computer Vision. Prentice Hall, New York (1982)Google Scholar
  2. 2.
    Tadeusiewicz, R., Flasiński, M.: Image Recognition. PWN, Warszawa (1991) (in Polish)Google Scholar
  3. 3.
    Saber, E., Xu, Y., Murat Tekalp, A.: Partial Shape Recognition by Sub-matrix Matching for Partial Matching Guided Image Labeling. Pattern Recognition 38, 1560–1573 (2005)CrossRefGoogle Scholar
  4. 4.
    Kiciak, P.: Modelling of curves and surfaces: applications in computer graphics. WNT, Warsaw (2005) (in Polish)Google Scholar
  5. 5.
    Soussen, C., Mohammad-Djafari, A.: Polygonal and Polyhedral Contour Reconstruction in Computed Tomography. IEEE Transactions on Image Processing 11(13), 1507–1523 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    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) (in Polish)Google Scholar
  7. 7.
    Tang, K.: Geometric Optimization Algorithms in Manufacturing. Computer - Aided Design & Applications 2(6), 747–757 (2005)Google Scholar
  8. 8.
    Choraś, R.S.: Computer Vision. Exit, Warszawa (2005) (in Polish)Google Scholar
  9. 9.
    Kozera, R.: Curve Modeling via Interpolation Based on Multidimensional Reduced Data. Silesian University of Technology Press, Gliwice (2004)Google Scholar
  10. 10.
    Rogers, D.F.: An introduction to NURBS with Historical Perspective. Morgan Kaufmann Publishers (2001)Google Scholar
  11. 11.
    Schumaker, L.L.: Spline Functions: Basic Theory. Cambridge Mathematical Library (2007)Google Scholar
  12. 12.
    Eckmann, B.: Topology, Algebra, Analysis- Relations and Missing Links. Notices of the American Mathematical Society 5(46), 520–527 (1999)MathSciNetGoogle Scholar
  13. 13.
    Citko, W., Jakóbczak, D., Sieńko, W.: On Hurwitz - Radon Matrices Based Signal Processing. In: Workshop Signal Processing at Poznań University of Technology (2005)Google Scholar
  14. 14.
    Tarokh, V., Jafarkhani, H., Calderbank, R.: Space-Time Block Codes from Orthogonal Designs. IEEE Transactions on Information Theory 5(45), 1456–1467 (1999)MathSciNetCrossRefGoogle Scholar
  15. 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. 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. 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. 18.
    Jakóbczak, D.: Shape Representation and Shape Coefficients via Method of Hurwitz-Radon Matrices. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds.) ICCVG 2010, Part I. LNCS, vol. 6374, pp. 411–419. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Jakóbczak, D.: Curve Interpolation Using Hurwitz-Radon Matrices. Polish Journal of Environmental Studies 3B(18), 126–130 (2009)Google Scholar
  20. 20.
    Jakóbczak, D.: Application of Hurwitz-Radon Matrices in Shape Representation. In: Banaszak, Z., Świć, A. (eds.) Applied Computer Science: Modelling of Production Processes, vol. 1(6), pp. 63–74. Lublin University of Technology Press, Lublin (2010)Google Scholar
  21. 21.
    Jakóbczak, D.: Object Modeling Using Method of Hurwitz-Radon Matrices of Rank k. In: Wolski, W., Borawski, M. (eds.) Computer Graphics: Selected Issues, pp. 79–90. University of Szczecin Press, Szczecin (2010)Google Scholar
  22. 22.
    Jakóbczak, D.: Implementation of Hurwitz-Radon Matrices in Shape Representation. In: Choraś, R.S. (ed.) Image Processing and Communications Challenges 2. AISC, vol. 84, pp. 39–50. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Jakóbczak, D.: Object Recognition via Contour Points Reconstruction Using Hurwitz-Radon Matrices. In: Józefczyk, J., Orski, D. (eds.) Knowledge-Based Intelligent System Advancements: Systemic and Cybernetic Approaches, pp. 87–107. IGI Global, Hershey (2011)Google Scholar
  24. 24.
    Jakóbczak, D.: Data Extrapolation and Decision Making via Method of Hurwitz-Radon Matrices. In: Jędrzejowicz, P., Nguyen, N.T., Hoang, K. (eds.) ICCCI 2011, Part I. LNCS (LNAI), vol. 6922, pp. 173–182. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dariusz Jakóbczak
    • 1
  • Witold Kosiński
    • 2
    • 3
  1. 1.Technical University of KoszalinKoszalinPoland
  2. 2.Polish-Japanese Institute of Information TechnologyWarsawPoland
  3. 3.Kazimierz-Wielki UniversityBydgoszczPoland

Personalised recommendations