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Physical variables in scale invariant systems often show chaotic, turbulent-like behavior, commonly associated to the existence of an underlying fractal or multifractal structure. However, the assessment of multifractality over experimental, discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the(More)
Real-world images are complex objects, difficult to describe but at the same time possessing a high degree of redundancy. A very recent study on the statistical properties of natural images reveals that natural images can be viewed through different partitions which are essentially fractal in nature. One particular fractal component, related to the most(More)
We show that the statistics of an edge type variable in natural images exhibits self-similarity properties which resemble those of local energy dissipation in turbulent flows. Our results show that self-similarity and extended self-similarity hold remarkably for the statistics of the local edge variance, and that the very same models can be used to predict(More)
Multiplicative cascades are often used to represent the structure of turbulence. Under the action of a multiplicative cascade, the relevant variables of the system can be understood as the result of a successive transfer of information in cascade from large to small scales. However, to make this cascade transfer explicit (i.e, being able to decompose each(More)
—A prerequisite for the successful retrieval of geophys-ical parameters from remote sensing measurements is the development of an accurate forward model. The European Space Agency Soil Moisture and Ocean Salinity (SMOS), carrying onboard an L-band interferometric radiometer (Microwave Interferometric Radiometer using Aperture Synthesis), was launched on(More)
Scale invariance is a fundamental property of ensembles of natural images 1]. Their non Gaussian properties 15, 16] are less well understood, but they indicate the existence of a rich statistical structure. In this work we present a detailed study of the marginal statistics of a variable related to the edges in the images. A numerical analysis shows that it(More)
In the latest years, multifractal analysis has been applied to image analysis. The multifractal framework takes advantage of multiscaling properties of images to decompose them as a collection of different fractal components, each one associated to a singularity exponent (an exponent characterizing the way in which that part of the image evolves under(More)
Natural images are complex but very structured objects and, in spite of its complexity, the sensory areas in the neocortex in mammals are able to devise learned strategies to encode them efficiently. How is this goal achieved? In this paper, we will discuss the multiscaling approach, which has been recently used to derive a redundancy reducing wavelet(More)