|dc.description.abstract||In recent years, new approaches to the problem of Automated Target Recognition
using techniques of shape theory and algebraic geometry have been explored. The
power of this shape theoretic approach is that it allows one to develop tests for
object/image matching that do not require knowledge of the object?s position in
relation to the sensor nor the internal parameters of the sensor. Furthermore, these
methods do not depend on the choice of coordinate systems in which the objects and
images are represented.
In this dissertation, we will expand on existing shape theoretic techniques and
adapt these techniques to new sensor models. In each model, we develop an appropriate
notion of shape for our objects and images and define the spaces of such shapes.
The goal in each case is to develop tests for matching object and image shapes under
an appropriate class of projections. The first tests we develop take the form of
systems of polynomial equations (the so-called object/image relations) that check for
exact matches of object/image pairs. Later, a more robust approach to matching is
obtained by defining metrics on the shape spaces. This allows us in each model to
develop a measure of ?how close? an object is to being able to produce a given image.
We conclude this dissertation by computing a number of examples using these tests
for object/image matching.||