Organizers:

Wendy Martinez, Wendy_Martinez@onr.navy.mil Edward J. Wegman (Chair), ewegman@galaxy.gmu.edu

Speakers

1:30 p.m.
Feature Detection in Spatial Point Processes with Application to Minefield Detection
Adrian Raftery, University of Washington

I will consider the "reconnaissance" minefield detection problem, in which a large area is surveyed and imaged, and potential mines identified. This typically leads to many false positives, and the task is to determine whether the area surveyed includes a minefield, and if so, where it is. We have found model-based clustering very useful for addressing this problem. The model used is a finite mixture of bivariate normal distributions, with possible cross-cluster constraints on the covariance matrices to represent, for example, high linearity. A Poisson process component is added to the mixture model to represent noise, or clutter. This has led to very good results in simulations based on specifications from the Naval Costal Systems Station, with detection rates around 95% or above, and low false positive rates. This work has also led to the MCLUST software which has been widely used in many applications.

I will review recent extensions of this work to curvilinear and nonparametric models using principal curves (similar to Kohonen self-organizing maps) and Voronoi tesselations. I will discuss various successful applications from imaging for automated textile manufacturing, medical image analysis, medical diagnosis, and the detection of seismic faults from earthquake catalogs, as well as minefield detection itself.

2:00 p.m.
Probabilistic Methods in Image Analysis with Applications in Automatic Target Recognition
Alan Willsky, Massachussetts Institute of Technology

In this talk we describe two different approaches to nonlinear image analysis and segmentation. The first of these, which can be thought of as a limiting form of so-called anisotropic diffusions results in a coupled set of differential equations with discontinuous right-hand sides. At each point in the evolution of this system, the image has been partitioned into a set of disjoint regions (starting from the trivial partition in which every pixel is a distinct region), and there is one DE for each such region. Thanks to the form of the RHS, the evolution causes regions to merge, producing a nested sequence of segmentations. Experimental results demonstrate the robustness of this algorithm to severe image degradations such as speckle. We will also describe the mathematical properties of these evolutions, their ties to robust edge-preserving priors, and the use of such an evolution for ML segmentation.

The other approach represents a new curve-evolution algorithm based explicitly on a statistical criterion. Curve evolution algorithms have received considerable attention recently for problems of segmentation and boundary finding. The general idea behind such methods is to devise a dynamical system for taking an initial curve and then evolving it to yield meaningful segmentations. Defining curves implicitly as the zero-crossing seg of an evolving surface leads to PDE evolutions for such surfaces which in turn lead to curve evolutions in which curves can merge, split, and change characteristics seamlessly. However, for the most part the method for designing these evolutions involved flows that only used local statistics around the current curve location, making these methods susceptible to noise and requiring ad hoc methods to specify either stopping rules or flow fields that would drive curves into areas in which boundaries were deemed likely (e.g., based on local gradient calculations). In our work, we begin from a global statistical formulation: we want to find curves which maximize the distance between a statistic (e.g., sample mean) calculated over the pixels inside the curve and the statistic calculated over pixels outside the curve. The result is a flow that is statistically based, makes explicitly use of smoothed, global statistics, and that yields remarkably robust segmentations of noisy images. Several extensions--to multiple regions and to a probabilisitc/curve evolution interpretation and implementation of the Mumford-Shah problem--will also be presented.

2:30 p.m.
Statistical Learning and Coarse-to-fine Object Detection
Donald Geman, University of Massachussetts

This talk is about research in computational vision which is motivated by parlor games such as "Twenty Questions" and involves a mixture of methods from statistics, information theory and image analysis. The approach will be illustrated by a learning-based approach to object detection. Random variables (image functionals) and search strategies are induced from data in a coarse-to-fine manner in both the complexity of the object representations and the exploration of poses and resolutions. The variables are selected based on purely statistical criteria; they have no a priori semantic or geometric interpretation. This naturally results in sparse, graded representations - coarse-to-fine templates. In addition, image regions are explored according to their information content, and as a result the spatial distribution of computation is very skewed. Experiments include detecting faces in natural scenes.