Ulf Grenander

Conditional-mean estimation via jump-diffusion processes in multiple target tracking/recognition

A new algorithm is presented for generating the conditional mean estimates of functions of target positions, orientations and type in recognition, and tracking of an unknown number of targets and target types. Taking a Bayesian approach, a posterior measure is defined on the tracking/target parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model, and a prior based on airplane dynamics. The Newtonian force equations governing rigid body dynamics are utilized to form the prior density on airplane motion. The conditional mean estimates are generated using a random sampling algorithm based on jump-diffusion processes for empirically generating MMSE estimates of functions of these random target positions, orientations, and type under the posterior measure. Results are presented on target tracking and identification from an implementation of the algorithm on a networked Silicon Graphics workstation and DECmpp/MasPar parallel machine.

Parameter estimation for constrained context-free language models

A new language model incorporating both N-gram and context-free ideas is proposed. This constrained context-free model is specified by a stochastic context-free prior distribution with N-gram frequency constraints. The resulting distribution is a Markov random field. Algorithms for sampling from this distribution and estimating the parameters of the model are presented.

Markov random field models for natural language

Markov chain (N-gram) source models for natural language were explored by Shannon and have found wide application in speech recognition systems. However, the underlying linear graph structure is inadequate to express the hierarchical structure of language necessary for encoding syntactic information. Context-free language models which generate tree graphs are a natural way of encoding this information, but lack the modeling of interword dependencies. We consider a hybrid tree/chain graph structure which has the advantage of incorporating lexical dependencies in syntactic representations. Two Markov random field probability measures are derived on these tree/chain graphs from the maximum entropy principle.

Membranes, mitochondria and amoebae: shape models

Most real-world shapes and images are characterized by high variability- they are not rigid, like crystals, for example—but they are strongly structured. Therefore, a fundamental task in the understanding and analysis of such image ensembles is the construction of models that incorporate both variability and structure in a mathematically precise way. The global shape models introduced in Grenanders general pattern theory are intended to do this. In this paper, we describe the representation of two-dimensional mitochondria and membranes in electron microscope photographs, and three-dimensional amoebae in optical sectioning microscopy. There are three kinds of variability to all of these patterns, which these representations accommodate. The first is the variability in shape and viewing orientation. For this, the typical structure is represented via linear, circular and spherical templates, with the variability accomodated via the application of transformations applied to the templates. The transformations...