A GEOMETRIC APPROACH TO STATISTICAL ANALYSIS OF CURVES

 Anuj Srivastava
 Department of Statistics
 Florida State University
 Tallahassee, FL 32306

Many applications in image analysis can benefit from a formal
statistical analysis of constrained curves. For instance, closed
curves denoting boundaries of imaged objects can be used for
characterizing, tracking, and recognizing objects. Also,
completion of hidden edges (of partially-obscured objects) can be
performed using elastic curves under first order boundary
conditions. We present a geometric approach to curve analysis,
consisting of the following steps: (i) define an appropriate space
of constrained curves, (ii) study the geometry of this space to
specify tangent spaces, projections and geodesics, and (iii) use
ordinary differential equations to solve for optimal curves. Not
only the geometry of curves, but also the geometry of the space of
curves is utilized. We apply this approach to clustering,
learning, and testing of planar shapes in images. Using prior
models on shape spaces, we present a Bayesian approach to
discovering shapes in high-clutter and partially obscured images.
We demonstrate these ideas using experimental results.

(This research is being performed in collaboration with Washington
Mio, Eric Klassen, and Xiuwen Liu)