Optimizing the Shape Parameters of Beta-Spline Using Particle Swarm Optimization
Keywords:Beta-Spline, Curve Fitting, Particle Swarm Optimization, Shape Parameters, 2D Font Image.
Beta-spline is an alternative curve for 2D font representation. It is preferred since it has G2 continuity and two shape parameters, that can be used to control the curve shape. These shape parameters can also be used to optimize the error between fitted curve and original data points. Commonly, most of the researcher use value of shape parameters of beta-spline as and or some of the researcher choose any random value of these two shape parameters that suitable to be used in beta-spline curve fitting. The values of shape parameters are very important since the values affect the total error of the fitted curves. Thus, in this paper, Particle Swarm Optimization (PSO) is employed to determine the optimum value of the two shape parameters that will optimize the approximation error of the fitted curve. The technique is applied on two fonts: Ù‰ and Î´, and tested using various number of iterations and populations.
 Hadi NA (2015), GÂ² parametric curve and surface fitting using beta-spline. Universiti Teknologi MARA.
 Koundinya GG, Jaikumar G, Akash, NR & Subramanian MSV (2012), Survey on digital image processing in sports. Research Journal of Applied Sciences, Engineering and Technology 4(24), 5552-5556.
 Sarfraz M, Irshad M & Hussain MZ (2012), Vectorization of image outlines using rational spline and genetic algorithm. International Proceedings of Computer Science and Information Technology 50, 16-20.
 Farin G (2014), Curves and surfaces for computer-aided geometric design: A practical guide. Elsevier.
 Park H & Lee JH (2007), B-spline curve fitting based on adaptive curve refinement using dominant points. Computer-Aided Design 39, 439-451.
 Liao CW & Huang JS (1991), Font generation by beta-spline curve. Computers and Graphics 15, 527-534.
 Yang HM, Lu JJ & Lee HJ (2001), A Bezier curve-based approach to shape description for Chinese calligraphy characters. Proceedings of the International Conference on Document Analysis and Recognition, pp. 276-280.
 Masood A & Sarfraz M (2008), An efficient technique for capturing 2D objects. Computers and Graphics 32, 93-104.
 Yahya F, Ali JM, Majid AA & Ibrahim A (2018), Automatic G 1 surface reconstruction from serial cross-sectional images. Proceedings of the International Conference on Advances in Visual Information Systems pp. 96-99.
 Sarfraz M & Khan M (2004), An automatic algorithm for approximating boundary of bitmap characters. Future Generation Computer Systems 20, 1327-1336.
 Hadi NA, Ibrahim A, Yahya F & Ali JM (2013), A comparative study on cubic bezier and beta-spline curves. Matematika 29, 55-64.
 Yang Q, Tian J & Si W (2017), An improved particle swarm optimization based on difference equation analysis. Journal of Difference Equations and Applications 23, 135-152.
 Barsky BA (1981), The beta-spline: A local representation based on shape parameters and fundamental geometric measures. Phd thesis, University of Utah.
 Barsky BA and Beatty JC (1983), Local control of bias and tension in beta-splines. Proceedings of the ACM SIGGRAPH Computer Graphics pp. 193-218.
 Mazlan NT (2017), Cubic beta-spline curve fitting using fuzzy interpolation. .
 Eberhart R & Kennedy J (1995), A new optimizer using particle swarm theory. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39-43.