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Pré-Publication, Document De Travail Année : 2017

Fractional Order Stochastic Image Integration Models and Deep Learning of Multi-Fractional Interactions

Résumé

The paper provides 3 main contributions for the analysis and simulation of fractionally integrated stochastic image fields. The first two contributions are dedicated to the definition of fields either directly on discrete spatial grids or by referring to continuous spatial frameworks. For the discrete spatial grid framework, the paper proposes a new class of fractionally integrated fields and derives their spectral characterizations, as well as a procedure for stochastic simulation of their samples. Concerning the continuous spatial framework, the paper proposes a stochastic integration framework for providing a sense to some classes of generalized fractional Brownian fields. For both continuous and spatial frameworks, a practical challenge is the determination of model intrinsic dimension in terms of minimum description length. In this respect, the paper addresses the identification of fractional singular frequency points (called poles), that is the number of interacting fractional integral operators, by designing a deep convolutional neural network trained on spectra of simulated multi-fractional textures. Dimensioning these multiple interactions is shown intricate due to the fact that fractionally integrated fields may exhibit infinite variances at several frequency points, leading to almost undistinguishable situations.
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Dates et versions

hal-01629345 , version 1 (06-11-2017)

Identifiants

  • HAL Id : hal-01629345 , version 1

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Abdourrahmane Atto. Fractional Order Stochastic Image Integration Models and Deep Learning of Multi-Fractional Interactions. 2017. ⟨hal-01629345⟩
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