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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)

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)

- J Isern-Fontanet, A Turiel, E García-Ladona, J Font
- 2006

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)

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)

- Antonio Turiel, Germán Mato, Néstor Parga, Jean-Pierre Nadal
- 1998

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)

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)

- Antonio Turiel, Né Stor Parga, Daniel L Ruderman, Thomas W Cronin
- 2000

Naive scale invariance is not a true property of natural images. Natural monochrome images possess a much richer geometrical structure, which is particularly well described in terms of multiscaling relations. This means that the pixels of a given image can be decomposed into sets, the fractal components of the image, with well-defined scaling exponents… (More)

It has been recently noticed that time series of returns in stock markets are of mul-tifractal (multiscaling) character. In that context, multifractality has been always evidenced by its statistical signature (i.e., the scaling exponents associated to a related variable). However, a direct geometrical framework, much more revealing about the underlying… (More)