The estimation of hölderian regularity using genetic programming

Abstract

This paper presents a Genetic Programming (GP) approach to synthesize estimators for the pointwise Holder 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 Holder 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 Holderian 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 Holder 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.