Diffeometric Anatomical Registrationon the Surface
Rachel A. Yotter1, Gabriel Ziegler1, Paul M. Thompson2, Christian Gaser1,3
1Department of Psychiatry, Friedrich-Schiller University, Jena, Germany
2Laboratory of Neuro Imaging, Department of Neurology, UCLA School of Medicine, Los Angeles, CA, USA
3Department of Neurology, Friedrich-Schiller University, Jena, Germany

Motivation

Results

Surface-based registration approaches may achieve higher
accuracy than volume-based approaches (Anticevic, 2008).
Furthermore, a registration approach that uses landmark featuresoften requires manual intervention, thus introducing adependency on the anatomist. Surface-based approaches mayeither be iterative or diffeomorphic. Diffeomorphic approaches
have the advantage that an exact inverse transformation can becalculated. Here, we adapt the volume-based diffeomorphic
DARTEL algorithm to the surface (Ashburner, 2007).

CURVATURESULCAL DEPTH

Methods
INITIALIZATION:• calculate shape index (SI) for highly smoothed source andtarget surfaces2⎛ k1 +k2 ⎞c = − arctan⎝ k1− k2 ⎠π• Re-parameterize target SI values onto source sphere &perform affine alignment using RMS error. Rotate sourcesphere.
�FOR run=1:3• FOR step=1:6• smooth and inflate surfaces… step=1::high-smoothing;step=3+::low-smoothing• calculate SI values for smoothed surfaces• re-parameterize source and target SI using regularlysampled points along θ and φ• solve flow field with 2D DARTEL using FMG solver• END• apply flow field to sphere, using
exponential weighting curve for poles

Above upper: T-maps formean curvature (left) and sulcal
depth (right).

Above lower: Residual meansquare for mean curvature(left) and sulcal depth (right).
Left: Histogram for meancurvature T-values. Larger
values indicate better match.
~15 minutes on a 2.4 GHz
iMac for a mesh with 150,000vertices
Left:Annotationfrom fsaveragetemplate,
resampled tosubjects space• for solution near poles: rotate all spheres by 90° along x-axis,
generate new SI maps, solve again with DARTEL, and rotate
back to original orientation• combine both solutions using φ-dependent
Gaussian weighting function• warped sphere is now input sphere
ENDFuture WorkValidate using manually-labeled surfaces (Dice coefficient).
“Biological” similarity using twin data. Explore solution directly on
the sphere (no reparameterization of individual subject data).
The above results are for shape index. It may be possible toachieve different analysis targets by using a different measurement
for the source and target maps, e.g., sulcal depth.

Acknowledgements
R.A.Y., G.Z., & C.G. are supported by the German BMBF grants
01EV0709 and 01GW0740. P.T. is supported by NIH grants
EB008432, EB008281, EB007813, HD050735.

ReferencesValidation••

74 T1-weighted MRI images for control subjects
T-value, residual mean square, and average maps forcurvature and sulcal depthcT(c) =•σ (c) 2Comparison with FreeSurfer (Fischl, 1999) and Spherical
Demons (Yeo, 2010) E-mail: rachel.yotter@uni-jena.deAnticevic, A. (2008) Comparing surface-based and volume-based analyese offunctional neuroimaging data in patients with schizophrenia. NeuroImage, 41, 835-848.
Ashburner, J. (2007) A fast diffeometric image registration algorithm. NeuroImage, 38,95-113.
Fischl, B. (1999) Cortical surface-based analysis: II. Inflation, flattening, and a surfacebased coordinate system. NeuroImage, 9(2), 195-207.
Yeo, B.T.T. (2010) Spherical Demons: Fast diffeomorphic landmark-free surface
registration. IEEE Transactions on Medical Imaging, 29(3), 650-668.

PDF available at: http://dbm.uni-jena.de/HBM2011/Yotter02.pdf