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Abstract:
The information about the objects in an image is almost exclusively
described by the higher-order interactions of its pixels. The Wiener
series is one of the standard methods to systematically characterize
these interactions. However, the classical estimation method of the
Wiener expansion coefficients via cross-correlation suffers from
severe problems that prevent its application to high-dimensional and
strongly nonlinear signals such as images. We propose an estimation
method based on regression in a reproducing kernel Hilbert space that
overcomes these problems using polynomial kernels as known from
Support Vector Machines and other kernel-based methods. Numerical
experiments show performance advantages in terms of convergence,
interpretability and system sizes that can be handled. By the time of
the conference, we will be able to present first results on the
higher-order structure of natural images.
