Sasaki Metrics for Analysis of Longitudinal Data on Manifolds.
Sasaki Metrics for Analysis of Longitudinal Data on Manifolds.
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DOI：
10.1109/cvpr.2012.6247780
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发表时间：
2012-06
期刊：
影响因子：
--
通讯作者：
Fletcher PT
中科院分区：
文献类型：
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作者：
Muralidharan P;Fletcher PT
纵向数据出现在许多应用程序中，这些应用程序的目标是了解单个实体随时间的变化。在这篇文章中，我们提出了一种分析取黎曼流形中值的纵向数据的方法。一个重要的应用是表征解剖形状的变化，并区分健康的解剖趋势和疾病引起的解剖趋势。我们提出了一个生成性分层模型，其中每个个体都由测地线趋势建模，而测地线趋势又被认为是种群平均测地线趋势的扰动。模型中的每条测地线都可以由起点和速度(即切线束中的一点)唯一地参数化。这些参数之间的比较是通过Sasaki度量实现的，该度量提供了切线束上的自然距离度量。通过将HotelingT2统计量推广到流形，我们对两组纵向数据之间的差异进行了统计假设检验。我们通过比较痴呆症受试者和健康老年对照组的纵向胼胝体数据，证明了这些方法能够区分形状变化的差异。
Longitudinal data arises in many applications in which the goal is to understand changes in individual entities over time. In this paper, we present a method for analyzing longitudinal data that take values in a Riemannian manifold. A driving application is to characterize anatomical shape changes and to distinguish between trends in anatomy that are healthy versus those that are due to disease. We present a generative hierarchical model in which each individual is modeled by a geodesic trend, which in turn is considered as a perturbation of the mean geodesic trend for the population. Each geodesic in the model can be uniquely parameterized by a starting point and velocity, i.e., a point in the tangent bundle. Comparison between these parameters is achieved through the Sasaki metric, which provides a natural distance metric on the tangent bundle. We develop a statistical hypothesis test for differences between two groups of longitudinal data by generalizing the Hotelling T2 statistic to manifolds. We demonstrate the ability of these methods to distinguish differences in shape changes in a comparison of longitudinal corpus callosum data in subjects with dementia versus healthily aging controls.