Using principal component analysis to enhance the generalized multifractal analysis approach to textural segmentation: Theory and application to microresistivity well logs

We introduce a new method to perform textural segmentation by mean of generalized multifractal analysis. This method can be applied to any signal or measure, self-similar or not. The main idea is to expand the log-generating function Φq(x) on a collection of basis functions denoted by Ψq,n(x). These functions are chosen to be the principal components of the collection of functions Φq(x) which is obtained from a sliding window analysis of a 1D-signal. This approach allows to represent texture with a minimal number of uncorrelated textural parameters. Significant improvements are obtained for the textural segmentation of dipmeter microresistivity well logs.