The visual estimation of object velocity in systems of tuned bilocal detector units (simplified Hassenstein Reichardt detectors) is investigated. The units contain delay filters of arbitrary low-pass characteristic. Arrays of such detector units with identical delay filters are assumed to cover the plane of analysis. The global evaluation of the output signals of suitably arranged detector units is exemplified by the analysis of frontoparallel translations of rigid objects. The correlative method permits the estimation of the instantaneous object velocity, independently of object form. The time course of the resulting estimate is shown to be the convolution of the true velocity profile with a time-invariant kernel that depends solely on the impulse response of the delay filters and thus characterizes the analyzer system. The mathematical analysis of the processing principle is illustrated by considering idealized detector systems. The response of correlative motion analyzers to compound motion and to motion of nonrigid objects is discussed.

Spatiotemporal relations that are represented by properly chosen multilinear forms of signal values are shown to be useful for form-independent motion analyses and for the extraction of form descriptors that are invariant under geometric transformations. Both tasks are performed by identical parallel computing ΣΠ-networks.

Two universal types of networks for the invariant recognition of pictorial patterns are compared with respect to function, structure and costs. The main stage of both networks serves for the extraction of features that are invariant under certain types of unrestricted geometric transformations, e.g. rigid translations. Both approaches are conceptualized for unequivocal class definitions and thus for the feasibility of perfect pattern reconstructions. Although the networks are structurally different, they are to a high degree functionally equivalent. The costs, i.e. the number of weights per class that must be adjusted in order to obtain ideal and invariant classification, turn out to be almost the same for both approaches as well as for the reference network (list classifier). In practice, however, the ΣΠ-network is superior to the TLU-network; it is more robust and even single invariant features are unequivocally defined. The investigations reported here do not concern any aspects of learning.

In this contribution principal problems of pattern recognition are outlined. Their consequences for biological, especially olfactory systems are explained and model concepts are assessed according to these basic facts.
Most often pattern recognition is identified with what is called classification or association, i.e. with the process of making decisions about the membership of, for example, odours to given classes of odours which in turn must be defined in terms of directly measurable properties (data) of the substances of interest. Classification means to compare individual data of substances with the definitions of all given classes and to decide which definition applies best to the data. The main task in pattern recognition is to define pattern classes by means of configurations and suitable combinations of a given number of independent elementary sensor-output signals (signal components or dimensions). — The maximum number of different pattern signals (e.g. odours) characterized by n components, each of m levels (intensity), is K = mⁿ.
The choice of class definitions depends on the number of classes and signal components, on the noise statistics of the measurements and on the degree of tolerable false classification. As usual, economic reasons largely determine the character and scope of class definitions. In conjunction with restrictions imposed by the data acquisition process, class definitions cause categorial interpretations of the actual substances.
Although the optimum methods for pattern classification are known they may be too costly to implement or may require too much time for their configuration. — A generally accepted size for appropriate learning samples is 5…10 patterns per synaptic coefficient and class which means that at least (5…10) n² typical patterns of every class must be presented for the creation of a rather powerful type of classifier (parabolic classifier).
However, there exist various computing structures for the mathematical recognition concepts. Thus, it would be interesting to find the model structure that fits best to the neural substrate.