### Statistical Shape Analysis of Target Boundaries in 2D Sonar Imagery

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 7, 2011 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Darshan Bryner – Naval Surface Warfare Center/FSU

There are several definitions of
the word shape; of these, the most
important to this research is “the external form or appearance of someone or
something as produced by its outline.”
Shape Analysis in this context focuses specifically on the mathematical
study of explicit, parameterized curves in 2D obtained from the boundaries of
targets of interest in Synthetic Aperture Sonar (SAS) imagery. We represent these curves with a
special “square-root velocity function,” whereby the space of all such
functions is a nonlinear Riemannian manifold under the standard L^2
metric. With this curve
representation, we form the mathematical space called “shape space” where a
shape is considered to be the orbit of an equivalence class under the group
actions of scaling, translation, rotation, and re-parameterization. It is in this quotient space that we can
quantify the distance between two shapes, cluster similar shapes into classes,
and form means and covariances of shape classes for statistical
inferences. In this particular
research application, I use this shape analysis framework to form probability
density functions on sonar target shape classes for use as a shape prior energy
term in a Bayesian Active Contour model for boundary extraction in SAS images. Boundary detection algorithms generally
perform poorly on sonar imagery due to their typically low signal to noise
ratio, high speckle noise, and muddled or occluded target edges; thus, it is
necessary that we use prior shape information in the evolution of an active
contour to achieve convergence to a meaningful target boundary.