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