Sparse Representations of Multiple Signals

We discuss the problem of finding sparse representations of a class of signals. We formalize the problem and prove it is NP-complete both in the case of a single signal and that of multiple ones. Next we develop a simple approximation method to the problem and we show experimental results using artificially generated signals. Furthermore,we use our approximation method to find sparse representations of classes of real signals, specifically of images of pedestrians. We discuss the relation between our formulation of the sparsity problem and the problem of finding representations of objects that are compact and appropriate for detection and classification.

A Self-Organizing Multiple-View Representation of 3D Objects

We explore representation of 3D objects in which several distinct 2D views are stored for each object. We demonstrate the ability of a two-layer network of thresholded summation units to support such representations. Using unsupervised Hebbian relaxation, we trained the network to recognise ten objects from different viewpoints. The training process led to the emergence of compact representations of the specific input views. When tested on novel views of the same objects, the network exhibited a substantial generalisation capability. In simulated psychophysical experiments, the network's behavior was qualitatively similar to that of human subjects.

A Computational Model for the Acquisition and Use of Phonological Knowledge

Does knowledge of language consist of symbolic rules? How do children learn and use their linguistic knowledge? To elucidate these questions, we present a computational model that acquires phonological knowledge from a corpus of common English nouns and verbs. In our model the phonological knowledge is encapsulated as boolean constraints operating on classical linguistic representations of speech sounds in term of distinctive features. The learning algorithm compiles a corpus of words into increasingly sophisticated constraints. The algorithm is incremental, greedy, and fast. It yields one-shot learning of phonological constraints from a few examples. Our system exhibits behavior similar to that of young children learning phonological knowledge. As a bonus the constraints can be interpreted as classical linguistic rules. The computational model can be implemented by a surprisingly simple hardware mechanism. Our mechanism also sheds light on a fundamental AI question: How are signals related to symbols?

Sparse Representations for Fast, One-Shot Learning

Humans rapidly and reliably learn many kinds of regularities and generalizations. We propose a novel model of fast learning that exploits the properties of sparse representations and the constraints imposed by a plausible hardware mechanism. To demonstrate our approach we describe a computational model of acquisition in the domain of morphophonology. We encapsulate phonological information as bidirectional boolean constraint relations operating on the classical linguistic representations of speech sounds in term of distinctive features. The performance model is described as a hardware mechanism that incrementally enforces the constraints. Phonological behavior arises from the action of this mechanism. Constraints are induced from a corpus of common English nouns and verbs. The induction algorithm compiles the corpus into increasingly sophisticated constraints. The algorithm yields one-shot learning from a few examples. Our model has been implemented as a computer program. The program exhibits phonological behavior similar to that of young children. As a bonus the constraints that are acquired can be interpreted as classical linguistic rules.

Equivalence and Reduction of Hidden Markov Models

This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements represent identical stochastic processes. This characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast algorithms to reduce HMMs to essentially unique and minimal canonical representations. The reduction to a canonical form leads to the definition of 'Generalized Markov Models' which are essentially HMMs without the positivity constraint on their parameters. We discuss how this generalization can yield more parsimonious representations of stochastic processes at the cost of the probabilistic interpretation of the model parameters.

Three-Dimensional Recognition of Solid Objects from a Two-Dimensional Image

This thesis addresses the problem of recognizing solid objects in the three-dimensional world, using two-dimensional shape information extracted from a single image. Objects can be partly occluded and can occur in cluttered scenes. A model based approach is taken, where stored models are matched to an image. The matching problem is separated into two stages, which employ different representations of objects. The first stage uses the smallest possible number of local features to find transformations from a model to an image. This minimizes the amount of search required in recognition. The second stage uses the entire edge contour of an object to verify each transformation. This reduces the chance of finding false matches.

Some Aspects of Pattern Recognition by Computer

A computer may gather a lot of information from its environment in an optical or graphical manner. A scene, as seen for instance from a TV camera or a picture, can be transformed into a symbolic description of points and lines or surfaces. This thesis describes several programs, written in the language CONVERT, for the analysis of such descriptions in order to recognize, differentiate and identify desired objects or classes of objects in the scene. Examples are given in each case. Although the recognition might be in terms of projections of 2-dim and 3-dim objects, we do not deal with stereoscopic information. One of our programs (Polybrick) identifies parallelepipeds in a scene which may contain partially hidden bodies and non-parallelepipedic objects. The program TD works mainly with 2-dimensional figures, although under certain conditions successfully identifies 3-dim objects. Overlapping objects are identified when they are transparent. A third program, DT, works with 3-dim and 2-dim objects, and does not identify objects which are not completely seen. Important restrictions and suppositions are: (a) the input is assumed perfect (noiseless), and in a symbolic format; (b) no perspective deformation is considered. A portion of this thesis is devoted to the study of models (symbolic representations) of the objects we want to identify; different schemes, some of them already in use, are discussed. Focusing our attention on the more general problem of identification of general objects when they substantially overlap, we propose some schemes for their recognition, and also analyze some problems that are met.