Seminar Details
2007-05-15 (14.00) : Statistical analysis of shapes of curves and surfaces
At Auditoire Euler
Organized by Mathematical Engineering
Speaker :
Srivastava, A.
Abstract :
We introduce a statistical framework for studying shapes of curves
and surfaces with applications in 2D and 3D image analysis. An important
tool for comparing and analyzing shapes is to
compute geodesics on shape spaces, under the chosen Riemannian
metrics. I will show two methods -- shooting and
path-straightening -- to compute geodesics on these spaces. Using
geodesics, one can define and compute sample statistics, impose
probability distributions, and study hypothesis testing involving
shapes. The case of analyzing shapes of surfaces, e.g. facial surfaces,
is much more difficult. Our approach is to represent a surface as an
indexed collection of curves and to extend ideas from curve analysis
to perform surface analysis. I will demonstrate this using a database
of facial surfaces.