Note: Different Date and Location
Abstract:
Elastic image registration can be described briefly as follows: Given so-called
template and patient images, one wishes to find a reasonable transformation
that makes the transformed template as similar as possible to the patient
image. Image registration problems are particularly prevalent in medical image
processing applications, for example registration of preoperative and
intraoperative image-guided surgical plans, finding anatomical aberrations
among populations of patients, tracking tumor morphology over time, and cardiac
motion
analysis. The problem of finding a reasonable transformation is ill-posed and is
usually treated by appropriate regularization. While elastic strain energy
regularization is often used, we reformulate the registration problem as an
optimal control problem. This allows the choice of a regularizer that acts
mainly in directions tangential to interfaces within the image. Since these
directions lie in the kernel of the Hessian, the minimizer (i.e. the registered
image) becomes almost independent of the regularization weight parameter.
To solve the resulting constrained optimization problems numerically, we apply
an inexact Gauss-Newton method. A multilevel approach is used to speed up the
iteration and to avoid local minima. The proposed methods are numerically
compared with elastic registration. We put a special emphasis on the regularity
of the transformation between template and patient image, since this is of
importance in most applications.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.