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Abstract:
Scale invariance is a fundamental property of ensembles of
natural images. Their non Gaussian properties 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 exhibits extended self-similarity.
This is a scaling property stronger than self-similarity: all its
moments can be expressed as a power of any given moment. More
interesting, all the exponents can be predicted in terms of a
multiplicative log-Poisson process. This is the very same model
that was used very recently to predict the correct exponents of the
structure functions of turbulent flows. These results allow us to
study the underlying multifractal singularities. In particular we
find that the most singular structures are one-dimensional: the
most singular manifold consists of sharp edges.
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