The estimation of Hölderian regularity using genetic programming

Leonardo Trujillo 1 Pierrick Legrand 2, 3 Jacques Lévy Véhel 4, 5, *
* Auteur correspondant
1 Instituto Tecnológico de Tijuana
2 IMB - Institut de Mathématiques de Bordeaux
3 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
4 Regularity - Probabilistic modelling of irregularity and application to uncertainties management
Inria Saclay - Ile de France
5 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
Abstract : This paper presents a Genetic Programming (GP) approach to synthesize estimators for the pointwise Hölder exponent in 2D signals. It is known that irregularities and singularities are the most salient and informative parts of a signal. Hence, explicitly measuring these variations can be important in various domains of signal processing. The pointwise Hölder exponent provides a characterization of these types of features. However, current methods for estimation cannot be considered to be optimal in any sense. Therefore, the goal of this work is to automatically synthesize operators that provide an estimation for the Hölderian regularity in a 2D signal. This goal is posed as an optimization problem in which we attempt to minimize the error between a prescribed regularity and the estimated regularity given by an image operator. The search for optimal estimators is then carried out using a GP algorithm. Experiments confirm that the GP-operators produce a good estimation of the Hölder exponent in images of multifractional Brownian motions. In fact, the evolved estimators significantly outperform a traditional method by as much as one order of magnitude. These results provide further empirical evidence that GP can solve difficult problems of applied mathematics.
keyword : Signal regularity Hölder exponent Genetic Programming
Type de document :
Communication dans un congrès
Genetic and Evolutionary Computation Conference (GECCO 2010). Best Paper Award in "Genetic Programming", Jul 2010, Portland Oregon, United States. ISBN 978-1-4503-0072-8, pp.861-868, 2010
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Leonardo Trujillo, Pierrick Legrand, Jacques Lévy Véhel. The estimation of Hölderian regularity using genetic programming. Genetic and Evolutionary Computation Conference (GECCO 2010). Best Paper Award in "Genetic Programming", Jul 2010, Portland Oregon, United States. ISBN 978-1-4503-0072-8, pp.861-868, 2010. 〈inria-00538943〉

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