Bo Markussen, Statistics Group at the Department of Natural
Sciences, Royal Veterinary and Agricultural University, Denmark.

Statistical Analysis of Image Warps using Stochastic
Differential Equations.

Abstract:

Imagine an image painted on a piece of rubber canvas. Stretching and
twisting this canvas the image is altered. Such alterations of an
image is what we understand by image warping. Mathematically a smooth
image warp can be encoded by a diffeomorphism of the plane into it
self. As known from differential geometry, a diffeomorphism can be
realized as the solution to the transport differential equation with
data given by a temporally changing velocity field. In this talk we
show how this framework can be used to derive a probabilistic model of
image warps. The key idea is to replace the deterministic differential
equation by a stochastic differential equation (in the Stratonovich
formulation). Having a probabilistic model at hand the tools of
classical statistic can be invoked for real life image warping
applications, e.g. 2D-electrophoresis gels. Our talk, however, will be
tilted towards theoretical considerations. In particular, the problems
of maximum a posteriori estimation (filtering/prediction) and maximum
likelihood estimation (parameter estimation) will be discussed.