Area Preserving Brain Mapping

Brain mapping transforms the brain cortical surface to canonical planar domains, which plays a fundamental role in morphological study. Most existing brain mapping meth-ods are based on angle preserving maps, which may in-troduce large area distortions. This work proposes an area preserving brain mapping method based on Monge-Brenier theory. The brain mapping is intrinsic to the Rie-mannian metric, unique, and diffeomorphic. The computa-tion is equivalent to convex energy minimization and power Voronoi diagram construction. Comparing to the exist-ing approaches based on Monge-Kantorovich theory, the proposed one greatly reduces the complexity (from n2 un-knowns to n), and improves the simplicity and efficiency. Experimental results on caudate nucleus surface map-ping and cortical surface mapping demonstrate the efficacy and efficiency of the proposed method. Conventional meth-ods for caudate nucleus surface mapping may suffer from numerical instability; in contrast, current method produces diffeomorpic mappings stably. In the study of cortical sur-face classification for recognition of Alzheimer’s Disease, the proposed method outperforms some other morphometry features. 1