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

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  • Saucier, Antoine
  • Muller, Jiri

Abstract

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.

Suggested Citation

  • Saucier, Antoine & Muller, Jiri, 2002. "Using principal component analysis to enhance the generalized multifractal analysis approach to textural segmentation: Theory and application to microresistivity well logs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 419-444.
    • Handle: RePEc:eee:phsmap:v:309:y:2002:i:3:p:419-444
    DOI: 10.1016/S0378-4371(02)00611-8
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