We construct a mixture of locally linear generative models of a collection of pixel-based images of digits, and use them for recognition. Different models of a given digit are used to capture different styles of writing, and new images are classified by evaluating their log-likelihoods under each model. We use an EMbased algorithm in which the M-step is computationally straightforward principal components analysis (PCA). Incorporating tangent-plane information [12] about expected local deformations only requires adding tangent vectors into the sample covariance matrices for the PCA, and it demonstrably improves performance.

This paper presents results from the first use of neural networks for the real-time feedback control of high temperature plasmas in a tokamak fusion experiment. The tokamak is currently the principal experimental device for research into the magnetic confinement approach to controlled fusion. In the tokamak, hydrogen plasmas, at temperatures of up to 100 Million K, are confined by strong magnetic fields. Accurate control of the position and shape of the plasma boundary requires real-time feedback control of the magnetic field structure on a timescale of a few tens of microseconds. Software simulations have demonstrated that a neural network approach can give significantly better performance than the linear technique currently used on most tokamak experiments. The practical application of the neural network approach requires high-speed hardware, for which a fully parallel implementation of the multilayer perceptron, using a hybrid of digital and analogue technology, has been developed.

Local algorithms such as K-nearest neighbor (NN) perform well in pattern recognition, even though they often assume the simplest distance on the pattern space. It has recently been shown (Simard et al. 1993) that the performance can be further improved by incorporating invariance to specific transformations in the underlying distance metric - the so called tangent distance. The resulting classifier, however, can be prohibitively slow and memory intensive due to the large amount of prototypes that need to be stored and used in the distance comparisons. In this paper we address this problem for the tangent distance algorithm, by developing rich models for representing large subsets of the prototypes. Our leading example of prototype model is a low-dimensional (12) hyperplane defined by a point and a set of basis or tangent vectors.

When training neural networks by the classical backpropagation algorithm the whole problem to learn must be expressed by a set of inputs and desired outputs. However, we often have high-level knowledge about the learning problem. In optical character recognition (OCR), for instance, we know that the classification should be invariant under a set of transformations like rotation or translation. We propose a new modular classification system based on several autoassociative multilayer perceptrons which allows the efficient incorporation of such knowledge. Results are reported on the NIST database of upper case handwritten letters and compared to other approaches to the invariance problem. 1 INCORPORATION OF EXPLICIT KNOWLEDGE The aim of supervised learning is to learn a mapping between the input and the output space from a set of example pairs (input, desired output). The classical implementation in the domain of neural networks is the backpropagation algorithm. If this learning set is sufficiently representative of the underlying data distributions, one hopes that after learning, the system is able to generalize correctly to other inputs of the same distribution.

The problem of interpolating between specified images in an image sequence is a simple, but important task in model-based vision. We describe an approach based on the abstract task of "manifold learning" and present results on both synthetic and real image sequences. This problem arose in the development of a combined lipreading and speech recognition system.

The efficiency of image search can be greatly improved by using a coarse-to-fine search strategy with a multi-resolution image representation. However, if the resolution is so low that the objects have few distinguishing features, search becomes difficult. We show that the performance of search at such low resolutions can be improved by using context information, i.e., objects visible at low-resolution which are not the objects of interest but are associated with them. The networks can be given explicit context information as inputs, or they can learn to detect the context objects, in which case the user does not have to be aware of their existence. We also use Integrated Feature Pyramids, which represent high-frequency information at low resolutions. The use of multiresolution search techniques allows us to combine information about the appearance of the objects on many scales in an efficient way. A natural fOlm of exemplar selection also arises from these techniques. We illustrate these ideas by training hierarchical systems of neural networks to find clusters of buildings in aerial photographs of farmland.

Deformable models are an attractive approach to recognizing nonrigid objects which have considerable within class variability. However, there are severe search problems associated with fitting the models to data. We show that by using neural networks to provide better starting points, the search time can be significantly reduced. The method is demonstrated on a character recognition task. In previous work we have developed an approach to handwritten character recognition based on the use of deformable models (Hinton, Williams and Revow, 1992a; Revow, Williams and Hinton, 1993). We have obtained good performance with this method, but a major problem is that the search procedure for fitting each model to an image is very computationally intensive, because there is no efficient algorithm (like dynamic programming) for this task. In this paper we demonstrate that it is possible to "compile down" some of the knowledge gained while fitting models to data to obtain better starting points that significantly reduce the search time. 1 DEFORMABLE MODELS FOR DIGIT RECOGNITION The basic idea in using deformable models for digit recognition is that each digit has a model, and a test image is classified by finding the model which is most likely to have generated it. The quality of the match between model and test image depends on the deformation of the model, the amount of ink that is attributed to noise and the distance of the remaining ink from the deformed model.

A fundamental open problem in computer vision-determining pose and correspondence between two sets of points in spaceis solved with a novel, robust and easily implementable algorithm. The technique works on noisy point sets that may be of unequal sizes and may differ by nonrigid transformations. A 2D variation calculates the pose between point sets related by an affine transformation-translation, rotation, scale and shear. A 3D to 3D variation calculates translation and rotation. An objective describing the problem is derived from Mean field theory. The objective is minimized with clocked (EMlike) dynamics. Experiments with both handwritten and synthetic data provide empirical evidence for the method. 1 Introduction

The human visual system can recognize various 3D (three-dimensional) objects from their 2D (two-dimensional) retinal images although the images vary significantly as the viewpoint changes. Recent computational models have explored how to learn to recognize 3D objects from their projected views (Poggio & Edelman, 1990). Most existing models are, however, based on supervised learning, i.e., during training the teacher tells which object each view belongs to. The model proposed by Weinshall et al. (1990) also requires a signal that segregates different objects during training. This paper, on the other hand, discusses unsupervised aspects of 3D object recognition where the system discovers categories by itself.

This paper presents a new method for image compression by neural networks. First, we show that we can use neural networks in a pyramidal framework, yielding the so-called PCA pyramids. Then we present an image compression method based on the PCA pyramid, which is similar to the Laplace pyramid and wavelet transform. Some experimental results with real images are reported. Finally, we present a method to combine the quantization step with the learning of the PCA pyramid. 1 Introduction In the past few years, a lot of work has been done on using neural networks for image compression, d. e.g.