Title :
Fractional Laplacian pyramids
Author :
Delgado-Gonzalo, Ricard ; Tafti, Pouya Dehghani ; Unser, Michael
Author_Institution :
Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland
Abstract :
We provide an extension of the L2-spline pyramid (Unser et al., 1993) using polyharmonic splines. We analytically prove that the corresponding error pyramid behaves exactly as a multi-scale Laplace operator. We use the multiresolution properties of polyharmonic splines to derive an efficient, non-separable filterbank implementation. Finally, we illustrate the potentials of our pyramid by performing an estimation of the parameters of multivariate fractal processes.
Keywords :
Laplace transforms; channel bank filters; fractals; image processing; splines (mathematics); L2 spline pyramid; error pyramid; fractional Laplacian pyramid; multiresolution property; multiscale Laplace operator; multivariate fractal process; nonseparable filterbank implementation; parameters estimation; polyharmonic spline; Biomedical imaging; Energy resolution; Filter bank; Fractals; Image processing; Laplace equations; Multiresolution analysis; Parameter estimation; Polynomials; Spline; Laplacian pyramids; fractals; multiresolution analysis; polyharmonic splines;
Conference_Titel :
Image Processing (ICIP), 2009 16th IEEE International Conference on
Conference_Location :
Cairo
Print_ISBN :
978-1-4244-5653-6
Electronic_ISBN :
1522-4880
DOI :
10.1109/ICIP.2009.5414306
