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The control of attention and of the associated saccadic fixations is to a large degree determined by the image content, that is, by salient local features in the image. The nature of this salient features and of the underlying strategy for their selection can be investigated within the context of natural scene statistics. For this, saccadic eye movements of human observers are recorded for a variety of natural and artificial test images, and the statistical properties of the fixated image regions are analyzed. The second-order statistics indicate that regions with higher spatial variance have a significantly higher probability to be fixated. Local contrast is therefore a salient feature. It was difficult to find additional differences in the local power spectra that can yield unequivocal information about a preference for specific local form properties. Differences that can be more easily interpreted as structural properties are derived from an investigation with higher-order statistics (bispectral density). The results indicate that nonredundant, intrinsically two-dimensional image features such as curved lines and edges, occlusions, isolated spots, and so on, play an important role in the saccadic selection process. Such features cannot be extracted by the classic spatial-frequency selective filter mechanisms but require nonlinear AND-like interactions between frequency components as possibly provided by end-stopping or hypercomplex properties related to the extraclassical receptive field.

Publisher Summary This chapter presents some arguments regarding the relevance of the concept of intrinsic dimensionality. It explains how intrinsic dimensionality is related to the statistical properties of natural images and to basic phenomena in visual neurophysiology and psychophysics. Related approaches in signal processing, with particular emphasis on the interpretation of images as surfaces are also discussed in. The chapter then presents the derivation of the conditions for the i2D selectivity of polynomial operators. It first illustrates that i2D operators cannot be linear and then considers the logical gating function of polynomial operators with respect to the processing of intrinsic dimensionality. The derivation of the necessary and sufficient conditions for quadratic i2D operators are also provided in this chapter. This chapter also presents examples of different types of i2D operators and discusses isotropic and orientation-selective versions of i2D operators, also exploring the relationship between intrinsic dimensionality and higher-order statistics.

A control strategy for expert systems is presented which is based on Shafer's Belief theory and the combination rule of Dempster. In contrast to well known strategies it is not sequentially and hypotheses-driven, but parallel and self-organizing, determined by the concept of information gain. The information gain, calculated as the maximal difference between the actual evidence distribution in the knowledge base and the potential evidence determines each consultation step. Hierarchically structured knowledge is an important representation form and experts even use several hierarchies in parallel for constituting their knowledge. Hence the control strategy is applied to a layered set of distinct hierarchies. Depending on the actual data one of these hierarchies is chosen by the control strategy for the next step in the reasoning process. Provided the actual data are well matched to the structure of one hierarchy, this hierarchy remains selected for a longer consultation time. If no good match can be achieved, a switch from the actual hierarchy to a competing one will result, very similar to the phenomenon of "restructuring" in problem solving tasks. Up to now the control strategy is restricted to multihierarchical knowledge bases with disjunct hierarchies. It is implemented in the expert system IBIG (inference by information gain), being presently applied to acquired speech disorders (aphasia).