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This research investigates two important topics having applications to the
analysis of spatial data. One topic of research is the development of 
inference procedures for a stochastic process that models the spatial
interrelation of point locations. An important defense application is where
the points represent mines, clutter, and other targets and non-targets in a
field of view. Here inference on the parameters of the point process 
modeling the spatial relationships can help determine whether a mine field 
is present or not. 

The second topic of research is the development of stochastic models and 
consequent fast algorithms for image segmentation and object detection. The 
principal class of stochastic models used are the partially ordered Markov 
models (POMMs) that are a subclass of Markov random fields. POMMs have 
already proved useful by providing straightforward inference and simulation 
procedures. We are developing further results in this regard for Bayesian 
spatial analysis of images. Segmentation is an important part of an image 
processing algorithm as it breaks the image into smaller components, which 
in turn are easier to process. In addition, the straightforward 
computational nature of the joint probability density functions for POMMs is 
well-suited to implement optimization procedures on images. We are 
developing object recognition algorithms that take advantage of this 
strength of POMMs. 

An important area of research that has immediate application to U.S. Navy 
and Marine operations is the detection of mine-like objects from images and 
the subsequent inference to determine whether those objects constitute a 
minefield. A mathematical abstraction of this problem is to a noisy spatial 
lattice process (the image) whose underlying signal is simply the union of a 
set of objects. Let the signal be further abstracted to a "grain-germ" 
stochastic process, where the germs are the locations of the grains (mines). 
The germs are considered here to be a spatial point process. Statistical 
image processing yields an estimate of the signal; then inference on the 
resulting stochastic processes (including the underlying point process) 
consists of estimating and testing associated parameters that determine 
whether a minefield is present or not. 

Another part of the research is to investigate and exploit the potential of
partially ordered Markov models (POMMs) for improving computational speed of
segmentation algorithms. Many segmentation techniques involve enormous
amounts of CPU time. Solutions for segmentation that require computation of
the joint probability density function, such as maximum likelihood or
Bayesian techniques, are especially computationally intensive. Thus,
alternative methods that reduce the computation time are highly desirable.
We are extending our results on supervised texture segmentation to
unsupervised segmentation. Unsupervised techniques require little or no user
intervention and are particularly useful in practical applications.
Segmentation using textures can be applied to distinguishing mines or
targets in data, as different classes of objects have different
characteristic textures. Segmentation using other criterion on which to
optimize, such as desired object characteristics, are also being
investigated.