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Implicit Volterra and Wiener Series for Higher-Order Image Analysis

MPS-Authors
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Franz,  MO
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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GfKl-2006-Franz.pdf
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Citation

Franz, M., & Schölkopf, B. (2006). Implicit Volterra and Wiener Series for Higher-Order Image Analysis. Poster presented at 30th Annual Conference of the German Classification Society: Advances in Data Analysis (GfKl 2006), Berlin, Germany.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D2A1-C
Abstract
The computation of classical higher-order statistics such as higher-order moments or spectra is difficult for images due to the huge number of terms to be estimated and interpreted. We propose an alternative approach in which multiplicative pixel interactions are described by a series of Wiener functionals. Since the functionals are estimated implicitly via polynomial kernels, the combinatorial explosion associated with the classical higher-order statistics is avoided. In addition, the kernel framework allows for estimating infinite series expansions and for the regularized estimation of the Wiener series. First results show that image structures such as lines or corners can be predicted correctly, and that pixel interactions up to the order of five play an important role in natural images.