Shape-Based Diffeomorphic Registration on Hippocampal Surfaces Using Beltrami Holomorphic Flow

Ronald Lok Ming Lui Harvard University Tsz Wai Wong University of California, Los Angeles Paul M. Thompson University of California, Los Angeles Tony F. Chan The Hong Kong University of Science and Technology Xianfeng Gu Stony Brook University Shing-Tung Yau Harvard University

Computational Geometry mathscidoc:1609.09034

Medical Image Computing and Computer Assisted Intervention, 323-330, 2010
We develop a new algorithm to automatically register hippocampal (HP) surfaces with complete geometric matching, avoiding the need to manually label landmark features. A good registration depends on a reasonable choice of shape energy that measures the dissimilarity between surfaces. In our work, we first propose a complete shape index using the Beltrami coefficient and curvatures, which measures subtle local differences. The proposed shape energy is zero if and only if two shapes are identical up to a rigid motion. We then seek the best surface registration by minimizing the shape energy. We propose a simple representation of surface diffeomorphisms using Beltrami coefficients, which simplifies the optimization process. We then iteratively minimize the shape energy using the proposed Beltrami Holomorphic flow (BHF) method. Experimental results on 212 HP of normal and diseased (Alzheimer's disease) subjects show our proposed algorithm is effective in registering HP surfaces with complete geometric matching. The proposed shape energy can also capture local shape differences between HP for disease analysis.
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@inproceedings{ronald2010shape-based,
  title={Shape-Based Diffeomorphic Registration on Hippocampal Surfaces Using Beltrami Holomorphic Flow},
  author={Ronald Lok Ming Lui, Tsz Wai Wong, Paul M. Thompson, Tony F. Chan, Xianfeng Gu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160906115603281197646},
  booktitle={Medical Image Computing and Computer Assisted Intervention},
  pages={323-330},
  year={2010},
}
Ronald Lok Ming Lui, Tsz Wai Wong, Paul M. Thompson, Tony F. Chan, Xianfeng Gu, and Shing-Tung Yau. Shape-Based Diffeomorphic Registration on Hippocampal Surfaces Using Beltrami Holomorphic Flow. 2010. In Medical Image Computing and Computer Assisted Intervention. pp.323-330. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160906115603281197646.
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