Hyperbolic harmonic brain surface registration with curvature-based landmark matching

Authors:
Rui Shi;Wei Zeng;Zhengyu Su;Yalin Wang;Hanna Damasio;Zhonglin Lu;Shing-Tung Yau;Xianfeng Gu
Affiliations:
Department of Computer Science, Stony Brook University;School of Computing & Information Sciences, Florida International University;Department of Computer Science, Stony Brook University;School of Computing, Informatics, and Decision Systems Engineering, Arizona State University;Neuroscience, University of Southern California;Department of Psychology, Ohio State University;Mathematics Department, Harvard University;Department of Computer Science, Stony Brook University
Venue:
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Year:
2013

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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.