IPMI 2013 - LNCS 7917

Hyperbolic Harmonic Brain Surface Registration with Curvature-Based Landmark Matching

Rui Shi¹, Wei Zeng², Zhengyu Su¹, Yalin Wang³, Hanna Damasio⁴, Zhonglin Lu⁵, Shing-Tung Yau⁶, and Xianfeng Gu¹

¹Department of Computer Science, Stony Brook University, USA
rshi@cs.stonybrook.edu
suzy.bryant@gmail.com
gu@cs.stonybrook.edu

²School of Computing & Information Sciences, Florida International University, USA
wzeng@cis.fiu.edu

³School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, USA
Yalin.Wang@asu.edu

⁴Neuroscience, University of Southern California, USA
hdamasio@college.usc.edu

⁵Department of Psychology, Ohio State University, USA
lu.535@osu.edu

⁶Mathematics Department, Harvard University, USA
yau@math.harvard.edu

Abstract. Brain Cortical surface registration is required for inter-subject studies of functional and anatomical data. Harmonic mapping has been applied for brain mapping, due to its existence, uniqueness, regularity and numerical stability. In order to improve the registration accuracy, sculcal landmarks are usually used as constraints for brain registration. Unfortunately, constrained harmonic mappings may not be diffeomorphic and produces invalid registration. This work conquer this problem by changing the Riemannian metric on the target cortical surface to a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism while the landmark constraints are enforced as boundary matching condition. The computational algorithms are based on the Ricci flow method and hyperbolic heat diffusion. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic, with higher qualities in terms of landmark alignment, curvature matching, area distortion and overlapping of region of interests.

LNCS 7917, p. 159 ff.

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