Abstract
This paper derives a new algorithm for piecewise linear approximation of n-dimensional parametric curves, specifically to be used with particle swarm optimization. The aim of the algorithm is to find the optimal piecewise linear approximation for a predefined number of segments. The performance of this algorithm is evaluated on a set of functions of varying dimensionality.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Burden, R.L. and Faires, J.D.: Numerical Analysis. Brooks Cole (2007)
Kennedy, J., Eberhart, R.C.: Particle Swarm Optimization. In: Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 1942–1948 (1995)
Kennedy, J., Mendes, R.: Population Structure and Particle Performance. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1671–1676 (2002)
Peer, E.S., van den Bergh, F., Engelbrecht, A.P.: Using Neighborhoods with the Guaranteed Convergence PSO. In: Proceedings of the IEEE Swarm Intelligence Symposium, pp. 235–242 (2003)
Sklansky, J., Gonzalez, V.: Fast polygonal approximation of digitized curves. Pattern Recognition 12(5), 327–331 (1980)
Salotti, M.: An efficient algorithm for the optimal polygonal approximation of digitized curves. Pattern Recognition Letters 22(2), 215–221 (2001)
do Carmo, M.: Differential Geometry of Curves and Surfaces. Prentice-Hall (1976)
Velho, L., de Figueiredo, L.H., Gomes, J.: Journal of the Brazilian Computer Society 3(3), 1–14 (1997)
Imamoto, A., Tang, B.: A Recursive Descent Algorithm for Finding the Optimal Minimax Piecewise Linear Approximation of Convex Functions. In: Advances in Electrical and Electronics Engineering, pp. 287–289 (2008)
Manis, G., Papakonstantinou, G., Tsanakas, P.: Optimal Piecewise Linear Approximation of Digitized Curves. In: Proceedings of International Conference on Digital Signal Processing, pp. 1079–1081 (1997)
Horst, J.A., Beichl, I.: A Simple Algorithm for Eficient Piecewise Linear Approximation of Space Curves. In: Proceedings of International Conference on Image Processing, pp. 744–747 (1997)
Pavlidis, T.: Polygonal Approximations by Newton’s Method. IEEE Transactions on Computers 25(8), 800–807 (1977)
Dunham, J.G.: Optimum uniform piecewise linear approximation of planar curves. IEEE Transactionson Pattern Analysis and Machine Intelligence PAMI-8(1), 67–75 (1986)
Stone, H.: Approximation of Curves by Line Segments. Mathematics of Computation 15(73), 40–47 (1961)
Engelbrecht, A.P.: Particle Swarm Optimization: Velocity Initialization. Accepted for IEEE Congress on Eevolutionary Computation (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cleghorn, C.W., Engelbrecht, A.P. (2012). Piecewise Linear Approximation of n-Dimensional Parametric Curves Using Particle Swarms. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2012. Lecture Notes in Computer Science, vol 7461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32650-9_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-32650-9_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32649-3
Online ISBN: 978-3-642-32650-9
eBook Packages: Computer ScienceComputer Science (R0)