Sains Malaysiana 44(8)(2015): 1203-1208

Pembinaan Semula Fon dengan Bézier Kubik Menggunakan Evolusi Pembezaan

(Reconstruction of Font with Cubic Bézier Using Differential Evolution)

NURSHAZNEEM ROSLAN* & ZAINOR RIDZUAN YAHYA

Institut Matematik Kejuruteraan (IMK), Universiti Malaysia Perlis (UniMAP), Kampus Pauh Putra

02600 Arau, Perlis Indera Kayangan, Malaysia

Diserahkan: 21 November 2014/Diterima: 9 April 2015

ABSTRAK

Pembinaan semula lengkung banyak digunakan dalam kejuruteraan balikan untuk menghasilkan lengkung. Dalam kajian ini, evolusi pembezaan (EP) digunakan untuk mencari nilai titik kawalan yang optimum bagi lengkung Bézier kubik. Nilai titik kawalan yang diperoleh akan digunakan dalam persamaan lengkung Bézier kubik dan jumlah ralat antara imej sebenar dengan lengkung parametrik yang baru dihitung dengan menggunakan jumlah ralat kuasa dua (JRKD).

Kata kunci: Evolusi pembezaan; jumlah ralat kuasa dua (JRKD); lengkung Bézier kubik; pembinaan semula lengkung

ABSTRACT

Curve reconstructions are widely used in reverse engineering to produce the curves. In this study, differential evolution (DE) is used to find the optimal value for the control points of cubic Bézier curve. The value of these control points will be used in the equation of cubic Bézier curve and the amount of the error between the actual images with the new parametric curve is calculated by using sum square error (SSE).

Keywords: Cubic Bézier curve; curve reconstruction; differential evolution; sum square error (SSE)

RUJUKAN

Arunachalam, V. 2008. Optimization using differential evolution. Water Resources Research Report. Book 22. The University of Western Ontario. Department of Civil and Environment Engineering.

Avrahami, G. & Pratt, V. 1991. Sub-pixel edge detection in character digitization. Raster Imaging and Digital Typography II pp: 54-64.

Das, S., Abraham, A. & Konar, A. 2008. Particle swarm optimization and differential evolution algorithms: Technical analysis, applications and hybridization perspectives. Advances of Computational Intelligence in Industrial Systems. Berlin, Heidelberg: Springer. pp. 1-38.

Gálvez, A. & Iglesias, A. 2013. Firefly Algorithm for Bézier curve approximation. Computational Science and Its Applications (ICCSA). 13th International Conference on IEEE. pp. 81-88.

Itoh, K. & Ohno, Y. 1993. A curve fitting algorithm for character fonts. Electronic Publishing 6(3): 195-205.

Mallipeddi, R., Suganthan, P.N., Pan, Q.K. & Tasgetiren, M.F. 2011. Differential evolution algorithm with ensemble of parameters and mutation strategies. Applied Soft Computing 11(2): 1679-1696.

Masood, A. & Sarfraz, M. 2009. Capturing outlines of 2D objects with Bézier cubic approximation. Image and Vision Computing 27(6): 704-712.

Pandunata, P. & Shamsuddin, S.M.H. 2010. Differential evolution optimization for Bézier curve fitting. Computer Graphics, Imaging and Visualization (CGIV), 2010 Seventh International Conference on IEEE. pp. 68-72.

Prado, R.S., Silva, R.C., Guimarães, F.G. & Neto, O.M. 2010. Using differential evolution for combinatorial optimization: A general approach. In Systems Man and Cybernetics (SMC), 2010 IEEE International Conference on IEEE. pp. 11-18.

Roslan, N. & Yahya, Z.R. 2014. Reconstruction of egg shape using cubic B-Spline. International Conference on Mathematics, Engineering & Industrial Application. 28-30 May. Penang. Preprint.

Rusdi, N.A. & Yahya, Z.R. 2014. Reconstruction of generic shape with cubic Bézier using Least Square Method. International Conference on Mathematics, Engineering & Industrial Applications 28-30 May. Penang. Preprint.

Salomon, D. 2007. Curves and Surfaces for Computer Graphics. New York: Springer.

Sarfraz, M., Irshad, M. & Hussain, M.Z. 2013. Reverse engineering of planar objects using GAs. Sains Malaysiana 42(8): 1167-1179.

Sarfraz, M. & Khan, M.A. 2004. An automatic algorithm for approximating boundary of bitmap characters. Future Generation Computer Systems 20(8): 1327-1336.

Sarfraz, M. & Khan, M.A. 2002. Automatic outline capture of Arabic fonts. Information Sciences 140(3): 269-281.

Sarfraz, M. & Razzak, M.F.A. 2002. An algorithm for automatic capturing of the font outlines. Computers & Graphics 26(5): 795-804.

Sarfraz, M. 2008a. Digital outline capture with cubic curves. Interactive Curve Modeling: With Applications to Computer Graphics, Vision and Image Processing. London: Springer-Verlag London Limited. pp. 267-295.

Sarfraz, M. 2008b. Corner detection for curve segmentation. Interactive Curve Modeling: With Applications to Computer Graphics, Vision and Image Processing. London: Springer-Verlag London Limited. pp. 209-240.

Storn, R. 1996. On the usage of differential evolution for function optimization. Fuzzy Information Processing Society, NAFIPS. Biennial Conference of the North American IEEE. pp. 519-523.

The MathWorks Inc. (MATLAB). 2014. Ramer-Douglas Peucker algorithm demo by Ligong Han, http://www.mathworks.com/ matlabcentral/fileexchange/41986-ramer-douglas-peucker-algorithm demo/content/DouglasPeucker.m

Yahya, Z.R. 2013. Representation of rational Bezier quadratics using genetic algorithm, differential evolution and particle swarm optimization. PhD Thesis. Universiti Malaysia Perlis (unpublished).

*Pengarang untuk surat-menyurat; email: nurshazneem@unimap.edu.my