Thursday, 14:15 - 14:40 h, Room: H 0111


Malik Kirchner
Large deformation diffeomorphic metric mapping using conforming adaptive finite elements

Coauthors: Andreas G√ľnther, Hans Lamecker, Martin Weiser


Automatic registration of anatomical objects is an important task in medical imaging.
One crucial prerequisite is finding a pointwise mapping between different shapes.

Currents are linear functionals providing a unified description of those shapes of any positive
integer dimension m ≤ d embedded in Rd.
The Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework [Joshi and Miller,
IEEE Transactions on Image Processing, 2000] solves the
correspondence problem between them by evolving a displacement field
along a velocity field.

In this talk we propose three aspects making this ODE/PDE optimization problem numerically practical.
We compute the temporal propagation of m-currents using a spatially discretized velocity field on
conforming adaptive finite elements. A hierarchical approach from coarse to fine lattices improves
performance and robustness of our method. The adaptive refinement process is driven by some residual
estimator based on the Riesz representative of shape differences.


Talk 3 of the invited session Thu.2.H 0111
"PDE optimization in medicine II" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]


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