Chapter title |
Riemannian Metric Optimization for Connectivity-Driven Surface Mapping
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Chapter number | 27 |
Book title |
Medical Image Computing and Computer-Assisted Intervention – MICCAI 2016
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Published in |
Lecture notes in computer science, October 2016
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DOI | 10.1007/978-3-319-46720-7_27 |
Pubmed ID | |
Book ISBNs |
978-3-31-946719-1, 978-3-31-946720-7
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Authors |
Jin Kyu Gahm, Yonggang Shi, Jin Kyu Gahm, Yonggang Shi |
Editors |
Sebastien Ourselin, Leo Joskowicz, Mert R. Sabuncu, Gozde Unal, William Wells |
Abstract |
With the advance of human connectome research, there are great interests in computing diffeomorphic maps of brain surfaces with rich connectivity features. In this paper, we propose a novel framework for connectivity-driven surface mapping based on Riemannian metric optimization on surfaces (RMOS) in the Laplace-Beltrami (LB) embedding space. The mathematical foundation of our method is that we can use the pullback metric to define an isometry between surfaces for an arbitrary diffeomorphism, which in turn results in identical LB embeddings from the two surfaces. For connectivity-driven surface mapping, our goal is to compute a diffeomorphism that can match a set of connectivity features defined over anatomical surfaces. The proposed RMOS approach achieves this goal by iteratively optimizing the Riemannian metric on surfaces to match the connectivity features in the LB embedding space. At the core of our framework is an optimization approach that converts the cost function of connectivity features into a distance measure in the LB embedding space, and optimizes it using gradients of the LB eigen-system with respect to the Riemannian metric. We demonstrate our method on the mapping of thalamic surfaces according to connectivity to ten cortical regions, which we compute with the multi-shell diffusion imaging data from the Human Connectome Project (HCP). Comparisons with a state-of-the-art method show that the RMOS method can more effectively match anatomical features and detect thalamic atrophy due to normal aging. |
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