multifractal

Tools (C/Matlab) for multifractal analysis of 1D (time-series) and 2D (images) signals

The material herein provides with low-level image processing filters that can be used for multifractal experiments/analyses of signals and images.

Description

The code source files will enable you to reproduce some of the experiments mentioned in the references below, namely for:

• multifractal analysis of signals/images using the so-called micro-wavelet,
• calculation of the multifractal singularity exponents and the multifractal spectrum,
• multifracal decomposition of signals/images,
• extraction of the so-called Most Singular Manifold,
• characterisation of the so-called chromatically reduced signal/image,
• multifractal reconstruction of signals/images.

See also singularity project for multifractal singularity analysis of 1D (time-series) signals.

Usage

To launch the programs:

• in Matlab, see also Contents.m for the whole list of functions; call run_multifractal.m for an example of application;
• in C, use the Makefile to build from source.

About

version	1.0 (non-active development)
since	2002
license	EUPL (cite the source code or any of the references below!)

References

• Yahia H., Turiel A., Chrysoulakis N., Grazzini J., Prastacos P., and Herlin I. (2008): Application of the multifractal microcanonical formalism to the detection of fire plumes in NOAA-AVHRR data, International Journal of Remote Sensing, 29(14):4189-4205, doi:10.1080/01431160701840174.
• Grazzini J., Turiel A., Yahia H., and Herlin I. (2007): A multifractal approach for extracting relevant textural areas in satellite meteorological images, Environmental Modelling & Software, 22(3):323-334, doi: 10.1016/j.envsoft.2005.07.032.
• Turiel A., Pérez-Vicente C.J., and Grazzini J. (2006): Numerical methods for the estimation of singularity spectra on sampled data: a comparative study, Journal of Computational Physics, 216(1):362-390, doi: 10.1016/j.jcp.2005.12.004.
• Grazzini J., Turiel A., and Yahia H. (2006): Multifractal formalism for remote sensing: A contribution to the description and the understanding of meteorological phenomena in satellite images, Complexus Mundi. Emergent Patterns in Nature, pp.247-256, World Scientific, doi: 10.1142/9789812774217_0022.
• Grazzini J. and Chrysoulakis N. (2005): Extraction of surface properties from a high accuracy DEM using multiscale remote sensing techniques, in Proc. EnviroInfo, pp.352-356.
• Turiel A., Grazzini J., and Yahia H. (2005): Multiscale techniques for the detection of precipitation using thermal IR satellite images, IEEE Geoscience and Remote Sensing Letters, 2(4):447-450, doi: 10.1109/LGRS.2005.852712.
• Grazzini J., Turiel A., and Yahia H. (2005): Presegmentation of high-resolution satellite images with a multifractal reconstruction scheme based on an entropy criterium, in Proc. IEEE ICPR, pp.I-649-52, doi: 10.1109/ICIP.2005.1529834.
• Grazzini J., Turiel A., Yahia H., and Herlin I. (2004): Edge-preserving smoothing of high-resolution images with a partial multifractal reconstruction scheme, in Proc. ISPRS, pp.1125-1129.
• Grazzini J. (2003): Analyses multiéchelle et multifractale d'images météorologiques : application à la détection de zones précipitantes (in French), Université de Marne-la-Vallée, PhD thesis.
• Grazzini J., and Turiel A., and Yahia H. (2002): Entropy estimation and multiscale processing in meteorological satellite images, in Proc. IEEE ICPR, vol. 3, pp.764-768, doi: 10.1109/ICPR.2002.1048103.
• Turiel A. and Parga, N. (2000): Multifractal wavelet filter of natural images, Physical Review Letters, 85(15):3325-8, doi:10.1103/PhysRevLett.85.3325.
• Turiel A. and Parga, N. (2000): The multifractal structure of contrast changes in natural images: From sharp edges to textures, Neural Computation, 12(4):763-793, doi:10.1162/089976600300015583.