Parameter Identification of 1D Recurrent Fractal Interpolation Functions with Applications to Imaging and Signal Processing

Authors:
Polychronis Manousopoulos;Vassileios Drakopoulos;Theoharis Theoharis
Affiliations:
Department of Informatics and Telecommunications, Theoretical Informatics, University of Athens, Athens, Greece 157 84;Department of Informatics and Telecommunications, Theoretical Informatics, University of Athens, Athens, Greece 157 84;Department of Informatics and Telecommunications, Theoretical Informatics, University of Athens, Athens, Greece 157 84
Venue:
Journal of Mathematical Imaging and Vision
Year:
2011

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Abstract

Recurrent fractal interpolation functions are very useful in modelling irregular (non-smooth) data. Two methods that use bounding volumes and one that uses the concept of box-counting dimension are introduced for the identification of the vertical scaling factors of such functions. The first two minimize the area of the symmetric difference between the bounding volumes of the data points and their transformed images, while the latter aims at achieving the same box-counting dimension between the original and the reconstructed data. Comparative results with existing methods in imaging applications are given, indicating that the proposed ones are competitive alternatives for both low and high compression ratios.