Parameter identification of 1D fractal interpolation functions using bounding volumes

Authors:
Polychronis Manousopoulos;Vassileios Drakopoulos;Theoharis Theoharis
Affiliations:
Department of Informatics and Telecommunications, Theoretical Informatics, University of Athens, Panepistimioupolis, 157 84, Athens, Greece;Department of Informatics and Telecommunications, Theoretical Informatics, University of Athens, Panepistimioupolis, 157 84, Athens, Greece;Department of Informatics and Telecommunications, Theoretical Informatics, University of Athens, Panepistimioupolis, 157 84, Athens, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

Fractal interpolation functions are very useful in capturing data that exhibit an irregular (non-smooth) structure. Two new methods to identify the vertical scaling factors of such functions are presented. In particular, they minimize the area of the symmetric difference between the bounding volumes of the data points and their transformed images. Comparative results with existing methods are given that establish the proposed ones as attractive alternatives. In general, they outperform existing methods for both low and high compression ratios. Moreover, lower and upper bounds for the vertical scaling factors that are computed by the first method are presented.