Title :
Area Preserving Brain Mapping
Author :
Zhengyu Su ; Wei Zeng ; Rui Shi ; Yalin Wang ; Jian Sun ; Xianfeng Gu
Author_Institution :
Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
Abstract :
Brain mapping transforms the brain cortical surface to canonical planar domains, which plays a fundamental role in morphological study. Most existing brain mapping methods are based on angle preserving maps, which may introduce large area distortions. This work proposes an area preserving brain mapping method based on Monge-Brenier theory. The brain mapping is intrinsic to the Riemannian metric, unique, and diffeomorphic. The computation is equivalent to convex energy minimization and power Voronoi diagram construction. Comparing to the existing approaches based on Monge-Kantorovich theory, the proposed one greatly reduces the complexity (from n2 unknowns to n ), and improves the simplicity and efficiency. Experimental results on caudate nucleus surface mapping and cortical surface mapping demonstrate the efficacy and efficiency of the proposed method. Conventional methods for caudate nucleus surface mapping may suffer from numerical instability, in contrast, current method produces diffeomorpic mappings stably. In the study of cortical surface classification for recognition of Alzheimer´s Disease, the proposed method outperforms some other morphometry features.
Keywords :
biomedical MRI; brain; medical image processing; Alzheimer´s Disease recognition; Monge-Brenier theory; Monge-Kantorovich theory; Riemannian metric; area preserving brain mapping; caudate nucleus surface mapping; convex energy minimization; cortical surface classification; cortical surface mapping; diffeomorpic mappings stably; numerical instability; power Voronoi diagram construction; Alzheimer´s disease; Brain mapping; Conformal mapping; Shape; Surface morphology; Vectors;
Conference_Titel :
Computer Vision and Pattern Recognition (CVPR), 2013 IEEE Conference on
Conference_Location :
Portland, OR
DOI :
10.1109/CVPR.2013.290