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We present a formalism that leads very naturally to a hierarchical description of the diierent contrast structures in images, providing precise deenitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points(More)
Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this Letter we show that those properties uniquely define an intrinsic wavelet and present a suitable technique to obtain it from an ensemble of images. Once this wavelet is known, images can be represented as expansions in 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 extended self-similarity remarkably holds for the statistics of the local edge variance, and that the very same models can be used to predict all the associated(More)
We report results on the scaling properties of changes in contrast of natural images in different visual environments. This study confirms the existence, in a vast class of images, of a multiplicative process relating the variations in contrast seen at two different scales, as was found in Turiel et al (Turiel A, Mato G, Parga N and Nadal J-P 1998(More)
Multifractal or multiaffine analysis is a promising new branch of methods in nonlinear physics for the study of turbulent flows and turbulentlike systems. In this Letter we present a new method based on the multifractal singularity extraction technique, the maximum singular stream-function method (MSSM), which provides a first order approximation to the(More)
In this paper we investigate the validity of the multifractal formalism to study sea surface temperature (SST). It is shown that SST patterns observed in moderate resolution SST images have anomalous scaling properties characteristic of a multifractal structure. The most probable origin of the observed structures is the turbulent character of the oceanic(More)
The local heat delivered by metallic nanoparticles selectively attached to their target can be used as a molecular surgery to safely remove toxic and clogging aggregates. We apply this principle to protein aggregates, in particular to the amyloid beta protein (Abeta) involved in Alzheimer's disease (AD), a neurodegenerative disease where unnaturally folded(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)