Publications

1993

• Multifractal tools for image processing
  
  • Lévy-Vehel Jacques
  • Berroir Jean-Paul
  , 1993, pp.209-216. A large class of segmentation processes is based on edge detection, often performed by gradient computation. This is reliable when one can approximate the signal by a differentiable function, which is not the case for singularities such as corners or junctions. Besides, one has to use different filters to detect step-edge or line singularity model. We present a method to detect those singularities based on multifractal theory. This approach presents several advantages: it allows to do all the computations directly on the discrete signal, without any underlying regularity hypothesis; we obtain a set of low level tools able to detect any kind of singularity; this method is reliable on natural images, as shown by a complete study of noise effect and examples on natural scenes.
• Image Analysis through Multifractal Description
  
  • Berroir Jean-Paul
  • Lévy-Vehel Jacques
  , 1993. This work is intended to provide a multifractal approach to the problem of edge detection in images. We show that an alternative description of images, based on the multifractal characterization of the signal, can be used instead of the classical approach that involves smoothing of the discrete data in order to compute derivatives. We focus on the study of edge detection using measures defined as functions of the grey level values in the neighborhood of a given pixel. Each measure is studied through the way it reacts to different types of edges and noise added to the image. Finally, we mention how the use of the multifractal spectrum (A, f(A)) may lead to a global approach to the problems of edge detection and region extraction.