Inhomogenous Scale Invariance


Image Credit: NASA image courtesy LANCE/EOSDIS MODIS Rapid Response Team at NASA GSFC

Multifractal analysis is now considered as a classical tool for signal/texture characterization. It notably permits to capture in a refined manner the detailed fluctuations of regularity of a texture along space and thus grounds texture characterization on the measurement of global and local smoothness.

The classical formulation of the multifractal formalism relies on the assumption that the multifractal properties of the process of interest are homogeneous. However, in many scenarios, it might happen that they could vary in time or in space. For instance, one faces this situation when dealing with the analysis of satellite photographs having both textures of clouds and snow.

The originality of this project is to

  • consider the study of inhomogeneous scale invariance as a joint problem of detection/segmentation
  • propose a formulation through the minimisation of functionals build around the total-variation penalty
  • Related Publications

    1. J. Frecon, N. Pustelnik, H. Wendt, L. Condat and P. Abry,
      Multifractal-based texture segmentation using variational procedure,
      Image, Video, and Multidimensional Signal Processing Workshop (IVMSP), 2016.
    2. J. Frecon, N. Pustelnik, H. Wendt and P. Abry,
      Multivariate Optimization for Multifractal-based Texture Segmentation,
      International Conference on Image Processing (ICIP), 2015.
    3. J. Frecon, N. Pustelnik, H. Wendt and P. Abry,
      Variation totale multivariee pour la detection de changement du spectre multifractal,
      Colloque francophone de traitement du signal et des images (GRETSI), 2015.