Implicit Wiener Series for Higher-Order Image Analysis

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. 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. Most of the interesting structure in a natural image is characterized by its higher-order statistics. Arbitrarily oriented lines and edges, for instance, cannot be described by the usual pairwise statistics such as the power spectrum or the autocorrelation function: From knowing the intensity of one point on a line alone, we cannot pre...

• Type: Conference
• Year: 2004
• Where: NIPS
• Authors: Matthias O. Franz, Bernhard Schölkopf
• Keywords: Huge Number, Image, NIPS 2004, NIPS 2007, Pixel Interactions