A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-tenn predict and to locate the outlines of the attractor by a new way of nonlinear principal component analysis. Closed-loop predictions are constrained to stay within these outlines, to prevent divergence from the attractor. Learning is exceptionally fast: parameter estimation for the 1000 sample laser data from the 1991 Santa Fe time series competition took less than a minute on a 166 MHz Pentium PC.

We develop a hierarchical generative model to study cue combination. The model maps a global shape parameter to local cuespecific parameters, which in tum generate an intensity image. Inferring shape from images is achieved by inverting this model. Inference produces a probability distribution at each level; using distributions rather than a single value of underlying variables at each stage preserves information about the validity of each local cue for the given image. This allows the model, unlike standard combination models, to adaptively weight each cue based on general cue reliability and specific image context.

A novel learning approach for human face detection using a network of linear units is presented. The SNoW learning architecture is a sparse network of linear functions over a predefined or incrementally learned feature space and is specifically tailored for learning in the presence of a very large number of features. A wide range of face images in different poses, with different expressions and under different lighting conditions are used as a training set to capture the variations of human faces. Experimental results on commonly used benchmark data sets of a wide range of face images show that the SNoW-based approach outperforms methods that use neural networks, Bayesian methods, support vector machines and others. Furthermore, learning and evaluation using the SNoW-based method are significantly more efficient than with other methods. 1 Introduction Growing interest in intelligent human computer interactions has motivated a recent surge in research on problems such as face tracking, pose estimation, face expression and gesture recognition. Most methods, however, assume human faces in their input images have been detected and localized.

The statistics of photographic images, when represented using multiscale (wavelet) bases, exhibit two striking types of non Gaussian behavior. First, the marginal densities of the coefficients have extended heavy tails. Second, the joint densities exhibit variance dependencies not captured by second-order models. We examine properties of the class of Gaussian scale mixtures, and show that these densities can accurately characterize both the marginal and joint distributions of natural image wavelet coefficients. This class of model suggests a Markov structure, in which wavelet coefficients are linked by hidden scaling variables corresponding to local image structure. We derive an estimator for these hidden variables, and show that a nonlinear "normalization" procedure can be used to Gaussianize the coefficients.

We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into conditional distributions of feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To fix this, we introduce hidden class labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters can be found with maximum likelihood estimation using the EM algorithm. We have obtained encouraging preliminary results on the problems of detecting various objects in SAR images and target recognition in optical aerial images. 1 Introduction

We describe a method for learning an overcomplete set of basis functions for the purpose of modeling sparse structure in images. The sparsity of the basis function coefficients is modeled with a mixture-of-Gaussians distribution. One Gaussian captures nonactive coefficients with a small-variance distribution centered at zero, while one or more other Gaussians capture active coefficients with a large-variance distribution. We show that when the prior is in such a form, there exist efficient methods for learning the basis functions as well as the parameters of the prior. The performance of the algorithm is demonstrated on a number of test cases and also on natural images.

Are there rules and principles that govern where the eyes are going to look next at each moment? In this paper, we sketch a theoretical framework based on information maximization to reason about the organization of saccadic eye movements.

The three-dimensional motion of humans is underdetermined when the observation is limited to a single camera, due to the inherent 3D ambiguity of 2D video. We present a system that reconstructs the 3D motion of human subjects from single-camera video, relying on prior knowledge about human motion, learned from training data, to resolve those ambiguities. After initialization in 2D, the tracking and 3D reconstruction is automatic; we show results for several video sequences. The results show the power of treating 3D body tracking as an inference problem.

Psychophysical and physiological evidence shows that sound localization of acoustic signals is strongly influenced by their synchrony with visual signals. This effect, known as ventriloquism, is at work when sound coming from the side of a TV set feels as if it were coming from the mouth of the actors. The ventriloquism effect suggests that there is important information about sound location encoded in the synchrony between the audio and video signals. In spite of this evidence, audiovisual synchrony is rarely used as a source of information in computer vision tasks. In this paper we explore the use of audio visual synchrony to locate sound sources. We developed a system that searches for regions of the visual landscape that correlate highly with the acoustic signals and tags them as likely to contain an acoustic source.

In this paper, we use mutual information to characterize the distributions of phonetic and speaker/channel information in a timefrequency space. The mutual information (MI) between the phonetic label and one feature, and the joint mutual information (JMI) between the phonetic label and two or three features are estimated. The Miller's bias formulas for entropy and mutual information estimates are extended to include higher order terms. The MI and the JMI for speaker/channel recognition are also estimated. The results are complementary to those for phonetic classification. Our results show how the phonetic information is locally spread and how the speaker/channel information is globally spread in time and frequency.