This directory contains the dissertation entitle 
"Geometry-Limited Diffusion" which was submitted by Ross T. Whitaker
to the University of North Carolina in October of 1993 for the 
partial fullfillment of the requirments of a Ph.D.  This work
was under the direction of Dr. Stephen M. Pizer.

This directory constains a set of poscript files which are the chapters 
of the dissertation.  The abstact for this document is given below.

				ABSTRACT

Ross T. Whitaker
"Geometry-Limited Diffusion"
Under the direction of Stephen M. Pizer

This paper addresses the problem of image segmentation and suggests that 
a number of interesting visual features can be specified as the boundaries 
of segments. It proposes a segmentation strategy that utilizes the local 
homogeneity of local image structure.  Stable differential measurements 
are made via a variable-conductance diffusion process, sometimes called 
anisotropic diffusion.  Anisotropic diffusion has been shown to preserve 
important image structure while reducing unwanted noise.

A multi-scale approach to variable-conductance diffusion is described.  
This technique combines information at a range of scales and provides a 
means of obtaining precise boundaries of ``large-scale'' objects in the 
presence of noise. These ideas generalize to incorporate multi-valued 
images and higher-order geometric structure.   The result is a framework for
constructing image segmentations based on the homogeneity of a set of
descriptors.   When applied to local image geometry, this method offers a
means of breaking images into geometric patches that have interesting 
visual features as boundaries.

Several examples of this framework are presented.  While the diffusion of 
intensity provides a means of detecting edges,  the diffusion of first-order 
information produces ridges and valleys.  A combination of of first- and 
second-order information provides a means of detecting the ``middles'' as 
well as the edges of objects.  A proof of the geometric invariance under 
orthogonal group transformations is given.  These same methods generalize 
to include systems of frequency-sensitive diffusion processes.  These systems 
are useful for characterizing patches based on texture.

An empirical investigation of these nonlinear diffusion processes shows 
they are stable in the presence of noise and offer distinct advantages over
conventional linear smoothing.  This analysis derives from a novel method 
for evaluating low-level computer-vision algorithms.  The method uses 
ensembles of stochastically generated images to compute a set of statistical 
metrics which quantify the accuracy and reliability of a process.  This 
evaluation offers a means of comparing different algorithms and exploring 
the space of free parameters associated with a single algorithm.