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Computationally efficient methods of approximations of the S-shape functions for image processing and computer graphics tasks

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Abstrakty
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The paper describes a number of methods for approximation of the S-shape functions, frequently used in computer graphics or image processing. The main focus is on efficient software and hardware implementations. We present original code for the high and low level languages which implement different approximations of the S-shape functions. Additionally we introduce the FixedFor <> template class which fills the gap of efficient representation of different length fixed-point data formats in C++.
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  • AGH University of Science and Technology, Al. Mickiewicza 30, Kraków 30-059, Poland, cyganek@agh.edu.pl
Bibliografia
  • [1] H. Amin, K. M. Curtis, B. R. Hayes-Gill, Piecewise linear approximation applied to nonlinear function of a neural network, IEE Proc-Circuits Devices Syst., 144(6):313-317, 1997
  • [2] K. Basterretxea, J. M. Tarela, and I. del Campo, Approximation of sigmoid function and the derivative for hardware implementation of artificial neurons, IEEEProc.-Circuits Devices Syst., 151(1):18-24, 2004
  • [3] B. Cyganek, S function software, http://home.agh.edu.pl/~cyganek/S.zip, 2011
  • [4] V. Kecman, Learning and Soft Computing: Support Vector Machines, Neural Networks, and Fuzzy Logic Models, MIT Press 2001
  • [5] I. Koren, Computer Arithmetic Algorithms, 2nd edition 2002
  • [6] J-M. Muller, Elementary Functions, Algorithms and Implementation 2nd edition, 2006
  • [7] C. Poynton, Digital Video and HDTV, Morgan-Kaufmann, 2007
  • [8] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C. The Art of Scientific Computing, Second Edition, Cambridge University Press, 1999
  • [9] M. T. Tommiska, Efficient digital implementation of the sigmoid function for reprogrammable logic, IEEE Proc.-Comput. Digit. Tech., 150(6):403-411, 2003
  • [10] M. Zhang, S. Vassiliadis, J. G. Delgado-Frias, Sigmoid Generators for Neural Computing Using Piecewise Approximations, IEEE Transactions On Computers, 45(9): 1045-1049, 1996
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bwmeta1.element.baztech-article-BAT5-0073-0012
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