Visual object recognition involves the identification of images of 3-D objects seenfrom arbitrary viewpoints. We suggest an approach to object recognition in which a view is represented as a collection of points given by their location in the image. An object is modeled by a set of 2-D views together with the correspondence between the views. We show that any novel view of the object can be expressed as a linear combination of the stored views. Consequently, we build a linear operator that distinguishes between views of a specific object and views of other objects.

During waking and sleep, the brain and mind undergo a tightly linked and precisely specified set of changes in state. At the level of neurons, this process has been modeled by variations of Volterra-Lotka equations for cyclic fluctuations of brainstem cell populations. However, neural network models based upon rapidly developing knowledge ofthe specific population connectivities and their differential responses to drugs have not yet been developed. Furthermore, only the most preliminary attempts have been made to model across states. Some of our own attempts to link rapid eye movement (REM) sleep neurophysiology and dream cognition using neural network approaches are summarized in this paper.

VOR neurons in normal and compensated animals.

Hand-printed digits can be modeled as splines that are governed by about 8 control points.

One way of simplifying neural networks so they generalize better is to add an extra t.erm

The complexity of learning in shallow I-Dimensional neural networks has been shown elsewhere to be linear in the size of the network. However, when the network has a huge number of units (as cortex has) even linear time might be unacceptable. Furthermore, the algorithm that was given to achieve this time was based on a single serial processor and was biologically implausible. In this work we consider the more natural parallel model of processing and demonstrate an expected-time complexity that is constant (i.e.

Connections between spline approximation, approximation with rational functions, and feedforward neural networks are studied. The potential improvement in the degree of approximation in going from single to two hidden layer networks is examined. Some results of Birman and Solomjak regarding the degree of approximation achievable when knot positions are chosen on the basis of the probability distribution of examples rather than the function values are extended.

It is shown that both changes in viewing position and illumination conditions can be compensated for, prior to recognition, using combinations of images taken from different viewing positions and different illumination conditions. It is also shown that, in agreement with psychophysical findings, the computation requires at least a sign-bit image as input - contours alone are not sufficient. 1 Introduction The task of visual recognition is natural and effortless for biological systems, yet the problem of recognition has been proven to be very difficult to analyze from a computational point of view. The fundamental reason is that novel images of familiar objects are often not sufficiently similar to previously seen images of that object. Assuming a rigid and isolated object in the scene, there are two major sources for this variability: geometric and photometric. The geometric source of variability comes from changes of view position. A 3D object can be viewed from a variety of directions, each resulting with a different 2D projection. The difference is significant, even for modest changes in viewing positions, and can be demonstrated by superimposing those projections (see Figure 1, first row second image). Much attention has been given to this problem in the visual recognition literature ([9], and references therein), and recent results show that one can compensate for changes in viewing position by generating novel views from a small number of model views of the object [10, 4, 8].

Another class of nonlinear algorithms, exemplified by CART (Breiman, Friedman, Olshen, & Stone, 1984) and MARS (Friedman, 1990), generalizes classical techniques by partitioning the training data into non-overlapping regions and fitting separate models in each of the regions. These two classes of algorithms extend linear techniques in essentially independent directions, thus it seems worthwhile to investigate algorithms that incorporate aspects of both approaches to model estimation. Such algorithms would be related to CART and MARS as multilayer neural networks are related to linear statistical techniques. In this paper we present a candidate for such an algorithm. The algorithm that we present partitions its training data in the manner of CART or MARS, but it does so in a parallel, online manner that can be described as the stochastic optimization of an appropriate cost functional.

Three methods for improving the performance of (gaussian) radial basis function (RBF) networks were tested on the NETtaik task. In RBF, a new example is classified by computing its Euclidean distance to a set of centers chosen by unsupervised methods. The application of supervised learning to learn a non-Euclidean distance metric was found to reduce the error rate of RBF networks, while supervised learning of each center's variance resulted in inferior performance. The best improvement in accuracy was achieved by networks called generalized radial basis function (GRBF) networks. In GRBF, the center locations are determined by supervised learning. After training on 1000 words, RBF classifies 56.5% of letters correct, while GRBF scores 73.4% letters correct (on a separate test set). From these and other experiments, we conclude that supervised learning of center locations can be very important for radial basis function learning.