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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.