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Implicit Volterra and Wiener Series for Higher-Order Image Analysis

2006

Conference Paper

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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.

Author(s): Franz, MO. and Schölkopf, B.
Book Title: Advances in Data Analysis: Proceedings of the 30th Annual Conference of The Gesellschaft für Klassifikation
Volume: 30
Pages: 1
Year: 2006
Month: March
Day: 0

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
State: Published

Links: PDF

BibTex

@inproceedings{3911,
  title = {Implicit Volterra and Wiener Series for Higher-Order Image Analysis},
  author = {Franz, MO. and Sch{\"o}lkopf, B.},
  booktitle = {Advances in Data Analysis: Proceedings of the 30th Annual Conference of The Gesellschaft f{\"u}r Klassifikation},
  volume = {30},
  pages = {1},
  organization = {Max-Planck-Gesellschaft},
  month = mar,
  year = {2006},
  month_numeric = {3}
}