Infinitely Divisible Cascades to Model the Statistics of Natural Images
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We propose to model the statistics of natural images thanks to the large class of stochastic processes called Infinitely Divisible Cascades (IDC). IDC were first introduced in one dimension to provide multifractal time series to model the socalled intermittency phenomenon in hydrodynamical turbulence. We have extended the definition of scalar infinitely divisible cascades from 1 to N dimensions and commented on the relevance of such a model in fully developed turbulence in [1]. In this article, we focus on the particular 2 dimensional case. IDC appear as good candidates to model the statistics of natural images. They share most of their usual properties and appear to be consistent with several independent theoretical and experimental approaches of the literature. We point out the interest of IDC for applications to procedural texture synthesis.
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Index Terms:
Stochastic processes, Picture/Image Generation,, Fractals, Image Processing and Computer Vision, Statistical, Image models
Citation:
Pierre Chainais, "Infinitely Divisible Cascades to Model the Statistics of Natural Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 12, pp. 2105-2119, June 2007, doi:10.1109/TPAMI.2007.1113
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