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Application of Hurwitz – Radon matrices in shape representation

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Computer vision needs suitable methods of shape representation and contour reconstruction. One of them, invented by the author and called method of Hurwitz-Radon Matrices (MHR), can be used in representation and reconstruction of shapes of the objects in the plane. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. Shape is represented by the set of nodes. It is shown how to create the orthogonal and discrete OHR operator 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.
Rocznik
Strony
63--74
Opis fizyczny
Bibliogr. 27 poz., fig.
Twórcy
  • Koszalin Technological University, ul. Śniadeckich 2, 75-453 Koszalin
Bibliografia
  • [1] BALLARD D.H.: Computer Vision, Prentice Hall, New York, 1982
  • [2] TADEUSIEWICZ R., FLASIŃSKI M.: Image Recognition, PWN, Warsaw, 1991
  • [3] SABER E., YAOWU XU, MURAT TEKALP A.: Partial shape recognition by submatrix matching for partial matching guided image labeling, Pattern Recognition 38 (2005), pp.1560-1573
  • [4] SEBASTIAN T.B., KLEIN P.N.: On aligning curves, IEEE Trans. Pattern Anal. Mach. Intell. 25 (1), 2003, pp. 116-124
  • [5] LIU T., GEIGER D.: Approximate tree matching and shape similarity, Int. Conf. Computer Vision, Corfu (Greece), 1999
  • [6] CHORAŚ R.S.: Komputerowa wizja, Exit, Warszawa, 2005
  • [7] 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
  • [8] LATECKI L.J., LAKAEMPER R.: Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution, Computer Vision and Image Understanding 3(73), 1999, pp. 441-454
  • [9] CIERNIAK R.: Tomografia komputerowa, Exit, Warszawa 2005
  • [10] SOUSSEN C., MOHAMMAD-DJAFARI A.: Polygonal and Polyhedral Contour Reconstruction in Computed Tomography. IEEE Transactions on Image Processing 11(13), 2004, pp. 1507-1523
  • [11] TANG K.: Geometric Optimization Algorithms in Manufacturing. Computer – Aided Design & Applications 2(6), 2005, pp. 747-757
  • [12] KOZERA R.: Curve Modeling via Interpolation Based on Multidimensional Reduced Data. Silesian University of Technology Press, Gliwice, 2004
  • [13] SCHUMAKER L. L.: Spline functions: basic theory. Cambridge Mathematical Library, 2007
  • [14] DEJDUMRONG N.: A shape preserving verification techniques for parametric curves. Computer Graphics, Imaging and Visualization, CGIV 2007, pp. 163-168
  • [15] DYN N., LEVIN D., GREGORY J. A.: A 4-point interpolatory subdivision scheme for curve design. Comput. Aided. Geom. Design, 4(1987), pp. 257–268
  • [16] ROGERS D. F.: An Introduction to NURBS with Historical Perspective. Morgan Kaufmann Publishers, 2001
  • [17] KICIAK P.: Podstawy modelowania krzywych i powierzchni. Zastosowania w grafice komputerowej, WNT, Warszawa, 2005
  • [18] JAKÓBCZAK D.: Curve Interpolation Using Hurwitz-Radon Matrices. Polish Journal of Environmental Studies, 3B(18), 2009, pp. 126-130
  • [19] DAHLQUIST G., BJOERCK A.: Numerical Methods. Prentice Hall, New York, 1974
  • [20] RALSTON A.: A First Course in Numerical Analysis. McGraw-Hill Book Company, New York, 1965
  • [21] ECKMANN B.: Topology, Algebra, Analysis- Relations and Missing Links. Notices of the American Mathematical Society 5(46), 1999, pp. 520-527
  • [22] CITKO W., JAKÓBCZAK D., SIEŃKO W.: On Hurwitz - Radon Matrices Based Signal Processing. Workshop Signal Processing at Poznan University of Technology, 2005
  • [23] TAROKH V., JAFARKHANI H., CALDERBANK R.: Space-Time Block Codes from Orthogonal Designs. IEEE Transactions on Information Theory 5(45), 1999, pp. 1456-1467
  • [24] SIEŃKO W., CITKO W., WILAMOWSKI B.: Hamiltonian Neural Nets as a Universal Signal Processor. 28th Annual Conference of the IEEE Industrial Electronics Society IECON, 2002
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  • [26] JAKÓBCZAK D.: 2D and 3D Image Modeling Using Hurwitz-Radon Matrices. Polish Journal of Environmental Studies 4A(16), 2007, pp. 104-107
  • [27] TADEUSIEWICZ R., KOROHODA P.: Komputerowa analiza i przetwarzanie obrazów. FPT, Kraków, 1997
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6992666d-18eb-4392-85e8-538ed41658a9
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