Optimized brain conformal parameterization using landmark constraint
Project Description:
To compare and integrate brain data, data from multiple subjects are
typically mapped into a canonical space. One method to do this is to conformally
map cortical surfaces to the sphere. It is well known that any genus zero
Riemann surface can be conformally mapped to a sphere. Therefore, conformal
mapping offers a convenient method to parameterize cortical surfaces without
angular distortion, generating an orthogonal grid on the cortex that locally
preserves the metric. To compare cortical surfaces more effectively, it
is advantageous to adjust the conformal parameterizations to match consistent
anatomical features across subjects. This matching of cortical patterns
improves the align- ment of data across subjects, although it is more challenging
to create a consistent conformal (orthogonal) parameterization of anatomy
across subjects when landmarks are constrained to lie at specific locations
in the spherical parameter space. Here we propose a new method, based on
a new energy functional, to optimize the conformal parameterization of cortical
surfaces by using landmarks. Experimental results on a dataset of 40 brain
hemispheres showed that the landmark mismatch energy can be greatly reduced
while effectively preserving conformality. The key advantage of this conformal
parameterization approach is that any local adjustments of the mapping to
match landmarks do not affect the conformality of the mapping significantly.
We also examined how the parameterization changes with different weighting
factors. As expected, the landmark matching error can be reduced if it is
more heavily penalized, but conformality is progressively reduced.
Publication:
- L.M. Lui,
Y. Wang, T.F. Chan and P.M. Thompson, "Landmark Constrained Genus Zero
Surface Conformal Mapping and Its Application to Brain Mapping Research",
Applied Numerical Mathematics 57, 2007, pp. 847-858
- Y. Wang, L.M. Lui, T.F. Chan and P.M. Thompson, "Optimization of Brain Conformal Mapping with Landmarks", Medical Image Computing and Computer-Assisted Internvention - MICCAI 2005: 8th International Conference, Palm Springs, CA USA, Oct. 26-29, 2005, Proceedings, Part II, pp. 675-683
Result:
