Nonlinear mechanisms and higher-order statistics in biological vision and electronic image processing: review and perspectives

Abstract

The classical approach in vision research—the derivation of basically linear filter models from experiments with simple artificial test stimuli—is currently undergoing a major revision. Instead of trying to keep the dirty environment out of our clean labs we put it now right into the focus of scientific exploration. An increasing number of scientists are using natural images in their experimental work, and concepts from statistics and information theory are employed for the theoretical modeling of the results. The new approach has a close relation to basic engineering strategies for electronic image processing, since its major concept is that biological sensory systems exploit the statistical redundancies of the environment by appropriate neural transformations. The standard engineering methods are not sufficient, however. Even such a basic biological feature as orientation selectivity requires the consideration of higher-order statistics, like multivariate wavelet statistics, cumulants, or polyspectra. Furthermore, there exists an abundance of nonlinear phenomena in biological vision, for example the phase invariance of complex cells, cortical gain control, end-stopping, and a variety of extra-classical receptive field properties. These amount to nonlinear combinations of linear wavelet filter outputs, which are required to exploit higher-order statistical dependencies, and make it necessary to consider unconventional modeling approaches like differential geometry or Volterra–Wiener systems. By use of such methods we cannot only gain a deeper understanding of the adaptation of the visual system to the complex natural environment, but we can also make the biological system an inspiring source for the design of novel strategies in electronic image processing.