Wavelet based Multifractal Analysis in Fractography

Abstract

In this paper, we propose a new method to identify three typically fracture surface morphologies based upon image analysis. The image is characterized via its multifractal spectrum, which mode yields the most frequent Holder exponent. Moreover, we recall the properties of several multifractal formalisms based on wavelet coefficients. In this context, we compare mathematically multifractal formalisms based on the wavelet transform modulus maxima approach and a new multifractal formalism based on wavelet leaders. It is shown that they compare very favourably to those obtained by wavelet coefficient based ones. Moreover, a practical extension to two dimensional signals (images) is validated. We illustrate this paper by some applications in fractography.