Novel Construction of Unbiased Templates for Brain Morphometry

总结（11/16/2019） 在这个项目中，我们开发了新的计算方法，用于大脑中的图像分析 结构变异性研究。所提出的方法是基于一个新的变分原理， 使用规定的雅可比行列式（对局部组织尺寸变化进行建模）构建变形 和规定的旋度向量（其对局部旋转进行建模）。 这项研究的目的是说服医学图像研究人员和用户，雅可比矩阵 行列式和旋度向量都应该在图像分析的所有步骤中使用。我们特别 发展： (1)基于雅可比行列式和旋度向量的一组变形的平均方法 新方法将平均值构造为变形，其雅可比行列式等于 平均的雅可比行列式和其旋度向量是平均的旋度向量。这个新 方法是生物学上有意义的;它还保留了集合中变形的可逆性。 (2)一种从图像集合中构造无偏模板的通用鲁棒方法。述的方法 开始于将该组中随机选择的图像配准到该组中的所有图像。然后重新采样 基于配准变形的平均值的初始模板是良好的近似;但是它可以 仍然偏向于初始模板。然后，我们重复平均过程以消除偏差， 得到无偏模板。计算实例显示旋度矢量的影响 和平均变形的方法的有效性和我们的方法， 无偏模板 该项目将大大提高我们分析大脑图像数据的能力;改善诊断，监测 以及脑部疾病和精神障碍的治疗。该项目有一个重要的培训和 教育成分。具体来说，一名博士生将参与算法设计、计算机代码 开发、测试和软件管理。

Summary (11/16/2019) In this project, we develop novel computational methods for image analysis with applications in brain structure variability studies. The proposed methods are based on a new Variational Principle which constructs a deformation with prescribed Jacobian determinant (which models local tissue size changes) and prescribed curl vector (which models local rotations). The goal of this research is to convince the medical image researchers and users that Jacobian determinant as well as curl vector should both be used in all steps of image analysis. Specifically, we develop: (1) A method of averaging a set of deformations based on Jacobian determinants and the curl vectors; the new method constructs the average as a deformation whose Jacobian determinant is equal to the average of the Jacobian determinants and whose curl vector is the average of curl vectors. This new method is biologically meaningful; it also preserves invertibilty of the deformations in the set. (2) A general robust method for construction of unbiased templates from a set of images. The method begins with registering a randomly chosen image in the set to all images in the set. Then the resample of the initial template on the average of the registration deformations is a good approximation; but it may still be biased toward the initial template. We then repeat the averaging process to remove bias and obtain unbiased template. Computational examples are presented to show the effects of curl vector and the effectiveness of method for averaging deformations and our method for construction of unbiased template. The project will significantly enhance our ability to analyze brain image data; improve diagnosis, monitor , and treatment of brain diseases and mental disorder. The project has an important training and educational component. Specifically, a PhD student will participate in algorithm design, computer code development, testing, and software management.