Jan Modersitzki (Lübeck): Hyperelastic Image Registration
Dienstag, 07.06.2011 17:15 im Raum N2
Image registration is one of the challenging problems in image processing, where ill-posedness is one of the
troublemakers and reasonable regularization is crucial. This talk presents hyperelasticity as a regularizer and
introduces a new and stable numerical implementation. On one hand, hyperelastic registration is an appropriate
model for large and highly non-linear deformations, for which a linear elastic model needs to fail. On the other
hand, the hyperelastic regularizer yields very regular and diffeomorphic transformations. While hyperelasticity
might be considered just an additional outstanding regularization option for some applications, it becomes
inevitable for applications involving higher order distance measures like mass-preserving registration.
The talk gives a short introduction to image registration and hyperelasticity. The hyperelastic image
registration problem is phrased in a variational setting and an existence proof for a solution is given.
However, the focus of the presentation is on a solid numerical scheme. A key challenge is an unbiased
discretization of hyperelasticity which enables the numerical monitoring of variations of length, surface and
volume of infinitesimal reference volumes. We resolve this issue by using a nodal based discretization with a
special tetrahedral partitioning.
The potential of the hyperelastic registration is demonstrated in a direct comparison with a linear elastic
registration on an academical example. The paper also presents a real life applications from 3D positron
emission tomography (PET) of the human heart which requires mass-preservation and thus hyperelastic registration
is an only option.