Curve Fitting by Fractal Interpolation
Fractal interpolation provides an efficient way to describe data that have an irregular or self-similar structure. Fractal interpolation literature focuses mainly on functions, i.e. on data points linearly ordered with respect to their abscissa. In practice, however, it is often useful to model curves as well as functions using fractal intepolation techniques. After reviewing existing methods for curve fitting using fractal interpolation, we introduce a new method that provides a more economical representation of curves than the existing ones. Comparative results show that the proposed method provides smaller errors or better compression ratios.
Keywordsfractal interpolation curve fitting iterated function systems
Unable to display preview. Download preview PDF.
- 1.Cochran, W.O., Hart, J.C., Flynn, P.J.: On approximating rough curves with fractal functions. Proc. Graphics Interface. 1, 65–72 (1998)Google Scholar
- 3.Mazel, D.S., Hayes, M.H.: Hidden-variable fractal interpolation of discrete sequences. Proc. Int. Conf. ASSP. 1, 3393–3396 (1991)Google Scholar
- 4.Uemura, S., Haseyama, M., Kitajima, H.: Efficient contour shape description by using fractal interpolation functions. IEEE Proc. ICIP. 1, 485–488 (2002)Google Scholar
- 6.Guérin, E., Tosan, E., Baskurt, A.: Fractal coding of shapes based on a projected IFS model. In: ICIP, vol. 2, pp. 203–206. IEEE Computer Society Press, Los Alamitos (2000)Google Scholar