Shape-based diffeomorphic registration on hippocampal surfaces using beltrami holomorphic flow

Authors:
Lok Ming Lui;Tsz Wai Wong;Paul Thompson;Tony Chan;Xianfeng Gu;Shing-Tung Yau
Affiliations:
Department of Mathematics, Harvard University, Cambridge, MA and Department of Mathematics, UCLA, Los Angeles, CA;Department of Mathematics, UCLA, Los Angeles, CA;Laboratory of Neuro Imaging, UCLA School of Medicine, Los Angeles, CA;Hong Kong University of Science and Technology, Hong Kong;Department of Computer Science, SUNY Stony Brook, Stony Brook, NY;Department of Mathematics, Harvard University, Cambridge, MA
Venue:
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Year:
2010

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Abstract

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.