Inverse problem for two-dimensional fractal sets using the wavelet transform and the moment method
- 1 January 1992
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 4 (15206149) , 665-668 vol.4
- https://doi.org/10.1109/icassp.1992.226310
Abstract
Fractal geometry has provided statistical and deterministic models for classes of signals and images that represent many natural phenomena and objects. Iterated function systems (IFS) theory provides a convenient way to describe and classify deterministic fractals in the form of a recursive definition. As a result, it is conceivable to develop image representation schemes based on the IFS parameters that correspond to a given fractal image. The authors propose the use of the wavelet transform and of the moment method for the solution of the inverse problem of recovering IFS parameters from fractal images. The redundancy of a fractal with respect to scale variation is mirrored by its wavelet decomposition, thus providing a method to estimate the scaling parameters for a class of IFSs modeling the image. Displacement parameters and probabilities are then found using the moment method. Experimental results verifying the approach are presented.Keywords
This publication has 10 references indexed in Scilit:
- IFS fractals and the wavelet transformPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Inverse problem for one-dimensional fractal measures via iterated function systems and the moment methodInverse Problems, 1990
- The wavelet transform, time-frequency localization and signal analysisIEEE Transactions on Information Theory, 1990
- Inverse problems in fractal construction: Moment method solutionPhysica D: Nonlinear Phenomena, 1990
- Wavelet analysis of the self-similarity of diffusion-limited aggregates and electrodeposition clustersPhysical Review A, 1990
- Inverse problem for fractal sets on the real line via the moment methodIl Nuovo Cimento B (1971-1996), 1989
- WaveletsPublished by Springer Nature ,1989
- An ergodic theorem for iterated mapsErgodic Theory and Dynamical Systems, 1987
- Iterated function systems and the global construction of fractalsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1985
- The Problem of MomentsPublished by American Mathematical Society (AMS) ,1943