Multifractal tools for image processing

• Main Authors: Lévy-Vehel, Jacques, Berroir, Jean-Paul
• Other Authors: Medical imaging and robotics (EPIDAURE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'Enseignement et de Recherche en Environnement Atmosphérique (CEREA), École des Ponts ParisTech (ENPC)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Kjell Arild Hogda and Bjorn Braathen and Karsten Heia
• Format: Conference Object
• Language: English
• Published: HAL CCSD 1993
• Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]; Norway; Tromso
• Online Access: https://hal.inria.fr/inria-00613998

International audience 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.