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

fYear

2009

fDate

7-10 Nov. 2009

Firstpage

3809

Lastpage

3812

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing (ICIP), 2009 16th IEEE International Conference on

Conference_Location

Cairo

ISSN

1522-4880

Print_ISBN

978-1-4244-5653-6

Electronic_ISBN

1522-4880

Type

conf

DOI

10.1109/ICIP.2009.5414306

Filename

5414306