Recognition of 3-D Objects from Multiple 2-D Views by a Self-Organizing Neural Architecture

The recognition of 3-D objects from sequences of their 2-D views is modeled by a neural architecture, called VIEWNET that uses View Information Encoded With NETworks. VIEWNET illustrates how several types of noise and varialbility in image data can be progressively removed while incornplcte image features are restored and invariant features are discovered using an appropriately designed cascade of processing stages. VIEWNET first processes 2-D views of 3-D objects using the CORT-X 2 filter, which discounts the illuminant, regularizes and completes figural boundaries, and removes noise from the images. Boundary regularization and cornpletion are achieved by the same mechanisms that suppress image noise. A log-polar transform is taken with respect to the centroid of the resulting figure and then re-centered to achieve 2-D scale and rotation invariance. The invariant images are coarse coded to further reduce noise, reduce foreshortening effects, and increase generalization. These compressed codes are input into a supervised learning system based on the fuzzy ARTMAP algorithm. Recognition categories of 2-D views are learned before evidence from sequences of 2-D view categories is accumulated to improve object recognition. Recognition is studied with noisy and clean images using slow and fast learning. VIEWNET is demonstrated on an MIT Lincoln Laboratory database of 2-D views of jet aircraft with and without additive noise. A recognition rate of 90% is achieved with one 2-D view category and of 98.5% correct with three 2-D view categories.National Science Foundation (IRI 90-24877); Office of Naval Research (N00014-91-J-1309, N00014-91-J-4100, N00014-92-J-0499); Air Force Office of Scientific Research (F9620-92-J-0499, 90-0083

Macrostate Data Clustering

We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to the metastable macroscopic states (macrostates) of a diffusive system. A "minimum uncertainty criterion" determines the linear transformation from eigenvectors to cluster-defining window functions. Eigenspectrum gap and cluster certainty conditions identify the proper number of clusters. The physically motivated fuzzy representation and associated uncertainty analysis distinguishes macrostate clustering from spectral partitioning methods. Macrostate data clustering solves a variety of test cases that challenge other methods.Comment: keywords: cluster analysis, clustering, pattern recognition, spectral graph theory, dynamic eigenvectors, machine learning, macrostates, classificatio

Evidence for fast thermalization in the plane-wave matrix model

We perform a numerical simulation of the classical evolution of the plane-wave matrix model with semiclassical initial conditions. Some of these initial conditions thermalize and are dual to a black hole forming from the collision of D-branes in the plane wave geometry. In particular, we consider a large fuzzy sphere (a D2-brane) plus a single eigenvalue (a D0-particle) going exactly through the center of the fuzzy sphere and aimed to intersect it. Including quantum fluctuations of the off-diagonal modes in the initial conditions, with sufficient kinetic energy the configuration collapses to a small size. We also find evidence for fast thermalization: rapidly decaying autocorrelation functions at late times with respect to the natural time scale of the system.Comment: 5 pages, 5 figures, revtex4 format; v2: minor typos fixed; v3: 8 pages, 9 figures, minor changes, includes a supplement as appeared on PR