CAREER: Statistical Models and Classification of Time-Varying Shape

本项目开发时变形状的非线性统计模型和分类程序，并研究其在生物医学图像分析问题中的应用。在生物学和医学中，理解改变解剖形状的过程往往是至关重要的。例如，研究婴儿大脑发育的神经科学家会对健康儿童和自闭症儿童的神经发育有何不同感兴趣。一个研究物种如何进化以适应环境的进化生物学家会对研究化石记录中发现的骨骼形状的变化感兴趣。该建模问题的挑战在于形状和形状变化是高度非线性和高维的，不能应用标准的线性统计。因此，建模和理解形状变化的能力取决于非线性空间中数据的新回归模型的发展。本项目的研究活动包括：(1)利用形状流形中的最小二乘原理开发处理时变形状的统计模型；(2)研究形状序列的新分类方法；(3)使用合成数据验证方法并测试其在阿尔茨海默病和自闭症神经影像学应用中的有效性。除了对计算机视觉、生物学和医学产生重大影响外，该项目还将微分几何、统计学和计算结合到本科和研究生计算机科学课程中。

This project develops nonlinear statistical models and classification procedures for time-varying shape and investigates their application to biomedical image analysis problems. In biology and medicine it is often critical to understand processes that change the shape of anatomy. For example, a neuroscientist studying the development of the infant brain would be interested in how neurodevelopment is different in healthy children versus those with Autism. An evolutionary biologist studying how a species has evolved to adapt to its environment would be interested in studying changes in the shape of bones found in the fossil record. The challenge in this modeling problem is that shape and shape variations are highly nonlinear and high-dimensional, and standard linear statistics cannot be applied. Therefore, the ability to model and understand changes in shape depends on the development of new regression models for data in nonlinear spaces. The research activities of this project include: (1) developing statistical models for dealing with time-varying shape using least-squares principles in shape manifolds, (2) investigating new classification methods for shape sequences, and (3) validating the methodology using synthetic data and testing its efficacy for neuroimaging applications in Alzheimer's disease and Autism. In addition to the significant impact to computer vision, biology, and medicine, this project is combining differential geometry, statistics, and computing within the undergraduate and graduate computer science curriculum.