Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis.
Shape Classification Using Wasserstein Distance for Brain Morphometry Analysis.
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DOI：
10.1007/978-3-319-19992-4_32
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Gu X
中科院分区：
文献类型：
--
作者：
Su Z;Zeng W;Wang Y;Lu ZL;Gu X
脑形态测量学研究在医学影像分析和诊断中起着重要的作用。本文基于均匀化理论和黎曼最优质量传递理论，提出了一种基于Wasserstein距离的脑皮层表面分类新框架。根据庞加莱均匀化定理，所有形状都可以共形变形为三个标准空间之一：单位球、欧几里得平面或双曲平面。均匀化地图将扭曲表面区域元素。面积失真因子给出了正则化空间的概率度量。黎曼流形上的所有概率测度构成了瓦瑟斯坦空间。给定任意2个概率测度，它们之间存在唯一的最优质量运输图，运输成本定义了它们之间的沃瑟斯坦距离。沃瑟斯坦距离给出了沃瑟斯坦空间的黎曼度规。它本质上测量形状之间的不相似性，因此具有形状分类的潜力。据我们所知，这是第一次将最优质量输运图引入一般黎曼流形。该方法基于测地线功率Voronoi图。与传统方法相比，我们的方法仅依赖黎曼度量，并且在刚性运动和缩放下是不变的，因此它本质上是测量形状距离的。对不同智商的脑皮层表面进行分类的实验结果证明了该方法的有效性。
Brain morphometry study plays a fundamental role in medical imaging analysis and diagnosis. This work proposes a novel framework for brain cortical surface classification using Wasserstein distance, based on uniformization theory and Riemannian optimal mass transport theory. By Poincare uniformization theorem, all shapes can be conformally deformed to one of the three canonical spaces: the unit sphere, the Euclidean plane or the hyperbolic plane. The uniformization map will distort the surface area elements. The area-distortion factor gives a probability measure on the canonical uniformization space. All the probability measures on a Riemannian manifold form the Wasserstein space. Given any 2 probability measures, there is a unique optimal mass transport map between them, the transportation cost defines the Wasserstein distance between them. Wasserstein distance gives a Riemannian metric for the Wasserstein space. It intrinsically measures the dissimilarities between shapes and thus has the potential for shape classification. To the best of our knowledge, this is the first work to introduce the optimal mass transport map to general Riemannian manifolds. The method is based on geodesic power Voronoi diagram. Comparing to the conventional methods, our approach solely depends on Riemannian metrics and is invariant under rigid motions and scalings, thus it intrinsically measures shape distance. Experimental results on classifying brain cortical surfaces with different intelligence quotients demonstrated the efficiency and efficacy of our method.