Area Preserving Brain Mapping

Zhengyu Su, Wei Zeng, Rui Shi, Yalin Wang, Jian Sun, Xianfeng Gu; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2013, pp. 2235-2242


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 MongeBrenier 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 n ,tunknowns 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.

Related Material

author = {Su, Zhengyu and Zeng, Wei and Shi, Rui and Wang, Yalin and Sun, Jian and Gu, Xianfeng},
title = {Area Preserving Brain Mapping},
booktitle = {Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2013}