A neural network model of motion segmentation by visual cortex is described. The model clarifies how preprocessing of motion signals by a Motion Oriented Contrast Filter (MOC Filter) is joined to long-range cooperative motion mechanisms in a motion Cooperative Competitive Loop (CC Loop) to control phenomena such as as induced motion, motion capture, and motion aftereffects. The total model system is a motion Boundary Contour System (BCS) that is computed in parallel with a static BCS before both systems cooperate to generate a boundary representation for three dimensional visual form perception. The present investigations clarify how the static BCS can be modified for use in motion segmentation problems, notably for analyzing how ambiguous local movements (the aperture problem) on a complex moving shape are suppressed and actively reorganized into a coherent global motion signal. 1 INTRODUCTION: WHY ARE STATIC AND MOTION BOUNDARY CONTOUR SYSTEMS NEEDED? Some regions, notably MT, of visual cortex are specialized for motion processing. However, even the earliest stages of visual cortex processing, such as simple cells in VI, require stimuli that change through time for their maximal activation and are direction-sensitive. Why has evolution generated regions such as MT, when even VI is change-sensitive and direction-sensitive? What computational properties are achieved by MT that are not already available in VI?

We study the evolution of the generalization ability of a simple linear perceptron with N inputs which learns to imitate a "teacher perceptron". The system is trained on p aN binary example inputs and the generalization ability measured by testing for agreement with the teacher on all 2N possible binary input patterns. The dynamics may be solved analytically and exhibits a phase transition from imperfect to perfect generalization at a 1. Except at this point the generalization ability approaches its asymptotic value exponentially, with critical slowing down near the transition; the relaxation time is ex (1 - y'a)-2.

There have been very few demonstrations ofthe application ofVLSI neural networks to real world problems. Yet there are many signal processing, pattern recognition or optimization problems where a large number of competing hypotheses need to be explored in parallel, most often in real time. The massive parallelism of VLSI neural network devices, with one multiplier circuit per synapse, is ideally suited to such problems. In this paper, we present preliminary results from our design for a real time robot navigation system based on VLSI neural network modules.

The learning time of a simple neural network model is obtained through an analytic computation of the eigenvalue spectrum for the Hessian matrix, which describes the second order properties of the cost function in the space of coupling coefficients. The form of the eigenvalue distribution suggests new techniques for accelerating the learning process, and provides a theoretical justification for the choice of centered versus biased state variables.

In this paper, after some introductory remarks into the classification problem as considered in various research communities, and some discussions concerning some of the reasons for ascertaining the performances of the three chosen algorithms, viz., CART (Classification and Regression Tree), C4.5 (one of the more recent versions of a popular induction tree technique known as ID3), and a multi-layer perceptron (MLP), it is proposed to compare the performances of these algorithms under two criteria: classification and generalisation. It is found that, in general, the MLP has better classification and generalisation accuracies compared with the other two algorithms. 1 Introduction Classification of data into categories has been pursued by a number of research communities, viz., applied statistics, knowledge acquisition, neural networks. In applied statistics, there are a number of techniques, e.g., clustering algorithms (see e.g., Hartigan), CART (Classification and Regression Trees, see e.g., Breiman et al). Clustering algorithms are used when the underlying data naturally fall into a number of groups, the distance among groups are measured by various metrics [Hartigan]. CART [Breiman, et all has been very popular among applied statisticians. It assumes that the underlying data can be separated into categories, the decision boundaries can either be parallel to the axis or they can be a linear combination of these axes!. Under certain assumptions on the input data and their associated lIn CART, and C4.5, the axes are the same as the input features

Multi-layer perceptrons are often slow to learn nonlinear functions with complex local structure due to the global nature of their function approximations. It is shown that standard multi-layer perceptrons are actually a special case of a more general network formulation that incorporates B-splines into the node computations. This allows novel spline network architectures to be developed that can combine the generalization capabilities and scaling properties of global multi-layer feedforward networks with the computational efficiency and learning speed of local computational paradigms. Simulation results are presented for the well known spiral problem of Weiland and of Lang and Witbrock to show the effectiveness of the Spline Net approach.

Competitive learning is an unsupervised algorithm that classifies input patterns into mutually exclusive clusters. In a neural net framework, each cluster is represented by a processing unit that competes with others in a winnertake-all pool for an input pattern. I present a simple extension to the algorithm that allows it to construct discrete, distributed representations. Discrete representations are useful because they are relatively easy to analyze and their information content can readily be measured. Distributed representations are useful because they explicitly encode similarity. The basic idea is to apply competitive learning iteratively to an input pattern, and after each stage to subtract from the input pattern the component that was captured in the representation at that stage. This component is simply the weight vector of the winning unit of the competitive pool. The subtraction procedure forces competitive pools at different stages to encode different aspects of the input. The algorithm is essentially the same as a traditional data compression technique known as multistep vector quantization, although the neural net perspective suggests potentially powerful extensions to that approach.

Empirically, generalization between a training and a test stimulus falls off in close approximation to an exponential decay function of distance between the two stimuli in the "stimulus space" obtained by multidimensional scaling. Mathematically, this result is derivable from the assumption that an individual takes the training stimulus to belong to a "consequential" region that includes that stimulus but is otherwise of unknown location, size, and shape in the stimulus space (Shepard, 1987). As the individual gains additional information about the consequential region-by finding other stimuli to be consequential or nOl-the theory predicts the shape of the generalization function to change toward the function relating actual probability of the consequence to location in the stimulus space. This paper describes a natural connectionist implementation of the theory, and illustrates how implications of the theory for generalization, discrimination, and classification learning can be explored by connectionist simulation. 1 THE THEORY OF GENERALIZATION Because we never confront exactly the same situation twice, anything we have learned in any previous situation can guide us in deciding which action to take in the present situation only to the extent that the similarity between the two situations is sufficient to justify generalization of our previous learning to the present situation. Accordingly, principles of generalization must be foundational for any theory of behavior. In Shepard (1987) nonarbitrary principles of generalization were sought that would be optimum in any world in which an object, however distinct from other objects, is generally a member of some class or natural kind sharing some dispositional property of potential consequence for the individual.

We introduce oriented non-radial basis function networks (ONRBF) as a generalization of Radial Basis Function networks (RBF)- wherein the Euclidean distance metric in the exponent of the Gaussian is replaced by a more general polynomial. This permits the definition of more general regions and in particular-hyper-ellipses with orientations. In the case of hyper-surface estimation this scheme requires a smaller number of hidden units and alleviates the "curse of dimensionality" associated kernel type approximators.In the case of an image, the hidden units correspond to features in the image and the parameters associated with each unit correspond to the rotation, scaling and translation properties of that particular "feature". In the context of the ONBF scheme, this means that an image can be represented by a small number of features. Since, transformation of an image by rotation, scaling and translation correspond to identical transformations of the individual features, the ONBF scheme can be used to considerable advantage for the purposes of image recognition and analysis.

Feature selection and creation are two of the most important and difficult tasks in the field of pattern classification. Good features improve the performance of both conventional and neural network pattern classifiers. Exemplar selection is another task that can reduce the memory and computation requirements of a KNN classifier.