Velocity constancy and models for wide-field visual motion detection in insects.

The tangential neurons in the lobula plate region of the flies are known to respond to visual motion across broad receptive fields in visual space. When intracellular recordings are made from tangential neurons while the intact animal is stimulated visually with moving natural imagery,we find that neural response depends upon speed of motion but is nearly invariant with respect to variations in natural scenery. We refer to this invariance as velocity constancy. It is remarkable because natural scenes, in spite of similarities in spatial structure, vary considerably in contrast, and contrast dependence is a feature of neurons in the early visual pathway as well as of most models for the elementary operations of visual motion detection. Thus, we expect that operations must be present in the processing pathway that reduce contrast dependence in order to approximate velocity constancy. We consider models for such operations, including spatial filtering, motion adaptation, saturating nonlinearities, and nonlinear spatial integration by the tangential neurons themselves, and evaluate their effects in simulations of a tangential neuron and precursor processing in response to animated natural imagery. We conclude that all such features reduce interscene variance in response, but that the model system does not approach velocity constancy as closely as the biological tangential cell.

A note on least-squares learning procedures and classification by neural network models.

Neural network models are considered as mathematical classifiers whose inputs comprise random variables generated according to arbitrary stationary class distributions, and the implication of learning based on minimization of sum-square classification error over a training set of these observations for which class assignments are absolutely determined is addressed. Expectations for network outputs in such cases are weighted least-squares approximations to a posteriori probabilities for the classes, which justifies interpretation of network outputs as indicating degree of confidence in class membership. The author demonstrates this with a straightforward proof in which class probability densities are regarded as primitives and which for simplicity does not rely on probability theory or statistics. The author cites more detailed results giving conditions for consistency of the estimators and discusses some issues relating to the suitability of neural network models and back-propagation training for approximation of conditional probabilities in classification tasks.

A constitutive model for two-dimensional soft tissues and its application to experimental data.

A constitutive relation proposed by Shoemaker (Ph.D. dissertation, 1984) to model the mechanical behavior of membraneous or two-dimensional soft tissues is described. Experiments by Schneider (Ph.D. dissertation, 1982) on human skin and Lee et al. (Am. J. Physiol., 249, H222-H230, 1985) on canine pericardium, and the application of the constitutive model to biaxial stress-strain data from these experiments, are discussed. Some experimental data and predictions of the model obtained by curvefitting are presented for comparison. Values of material parameters are also presented. It is concluded that the constitutive model is well able to fit results of individual tests, and that its generality (judged by consistency of parameters from test to test of the same specimen), though not complete, does compare favorably with some other results presented in the literature.