Wavelet leaders and bootstrap for multifractal analysis of images

Multifractal analysis is considered a promising tool for image processing, notably for texture characterization. However, practical operational estimation procedures based on a theoretically well established multifractal analysis are still lacking for image (as opposed to signal) processing. Here, a wavelet leader based multifractal analysis, known to be theoretically strongly grounded, is described and assessed for 2D functions (images). By means of Monte Carlo simulations conducted over both self-similar and multiplicative cascade synthetic images, it is shown here to benefit from much better practical estimation performances than those obtained from a 2D discrete wavelet transform coefficient analysis. Furthermore, this is complemented by the original analysis and design of procedures aiming at practically assessing and handling the theoretical function space embedding requirements faced by multifractal analysis. In addition, a bootstrap based statistical approach developed in the wavelet domain is proposed and shown to enable the practical computation of accurate confidence intervals for multifractal attributes from a given image. It is based on an original joint time and scale block non-parametric bootstrap scheme. Performances are assessed by Monte Carlo simulations. Finally, the use and relevance of the proposed wavelet leader and bootstrap based tools are illustrated at work on real-world images.

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