Abstract

The aim of the FRACTALES group is to develop theoretical tools in the field of fractal geometry, in order to finely analyze complex signals, for purposes of modelization, prediction, and synthesis.

More precisely, the FRACTALES group is concerned with the following aspects of fractal geometry :

• multifractal theory,
• iterated functions system,
• fractionnal stable processes.

• 1D signals :
  • road traffic analysis : we model some types of road traffic signals as noisy stochastic multiplicative cascades, and compute multifractal correlations on them,
  • financial analysis : we model financial time series as fractional stable processes,
  • speech synthesis : we model speech signals as attractors of IFS.
• 2D signals : we have designed a multifractal approach to the problem of image analysis. Defining various measures and capacities on an image, we are able to perform robust and precise image segmentation, data fusion, and image compression.

For most of these subjects, the FRACTALES group has active collaborations with other research groups in France, Europe and the U.S.A., and industrial contracts with french companies.