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Bicubic Splines in Problems of Modeling of Multidimensional Signals

  • Bahramov, Sayfiddin (Department of Computer Science and Mathematical Modeling, Uzbek National University) ;
  • Jovliev, Sanjar (Tashkent University of Information Technologies)
  • 투고 : 2011.07.21
  • 심사 : 2011.08.10
  • 발행 : 2011.08.31

초록

The paper is devoted to problem of spline modeling of multidimensional signals. A new method of nodes location for curves and surfaces computer construction in multidimensional spaces by means of B-splines is presented. The criteria are which links a square-mean error caused by high frequency spline distortions and approximation intervals is determined and necessary theorem is proved. In this method use a theory of entire multidimensional spectra and may be extended for the spaces of three, four and more variables.

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참고문헌

  1. Isroilov M. "Calculation metods" Part I. T.: Uzbekistan, 2003.
  2. Zavyalov U.S., Kvasov B.I., Miroshnichenko V.L. "Methods of spline-functions" M.: Nauka, 1980.
  3. Zaynidinov H.N., Hamdamov U.R. Roundoff Errors at a Parallelizing of Evaluations by Systems of Basic Splines. / Proceedings The Second International Conference on Mobile Computing, Communications and Applications (ICMOCCA2007). Tashkent, UZBEKISTAN, September 26-28, 2007, p. 95-98
  4. Smith S.W.: The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Publishing, San Diego. 2000.
  5. P. Litwinowicz and L. Williams, "Animating Images with Drawings Computer Graphics (Proc. SIGGRAPH '94), pp. 409-412, 1994
  6. E. Arge, M. $D\aehlen$, and A. Tveito, "Approximation of Scattered Data Using Smooth Grid Functions," J. Computational and Applied Math., vol. 59, pp. 191-205, 1995. https://doi.org/10.1016/0377-0427(94)00033-W
  7. R. Barnhill, "Representation and Approximation of Surfaces," J.R. Rice, ed., Mathematical Software III, pp. 68-119. New York: Academic Press, 1977.
  8. I. Cohen, L. D. Cohen, and N. Ayache. Using Deformable Surfaces to Segment 3-D Images and Infer Differential Structures. Computer Vision, Graphics and Image Processing: Image Understanding, 56(2):p. 242-263, September 1992.
  9. Hadenfeld, J., Local energy fairing of B-spline surfaces, in Mathematical Methods for Curves and Surfaces, Morten $D\frac{1}{2}hlen$, Tom Lyche, Larry L. Schumaker (eds.), Vanderbilt University Press, Nashville & London, 1995, p. 203-212.