Novel Construction of Unbiased Templates for Brain Morphometry

摘要(2019/11/16) 在这个项目中，我们为图像分析开发了新的计算方法，并将其应用于大脑 结构可变性研究。所提出的方法基于一种新的变分原理，该原理 使用指定的雅可比行列式构建变形(对局部组织大小变化进行建模) 和规定的卷曲向量(对局部旋转进行建模)。 这项研究的目的是让医学图像研究人员和用户相信雅可比 在图像分析的所有步骤中都应该使用行列式和旋度矢量。具体来说，我们 发展： (1)基于雅可比行列式和旋度向量对一组变形进行平均的方法； 新方法将平均值构造为雅可比行列式等于 雅可比行列式的平均值，其旋度向量是旋度向量的平均值。这是一项新的 方法具有生物学意义；它还保留了集合中变形的可逆性。 (2)一种从一组图像构造无偏模板的通用稳健方法。方法 从将集合中随机选择的图像配准到集合中的所有图像开始。然后，重新采样 平均配准变形的初始模板是一个很好的近似值；但它可以 仍然偏向于初始模板。然后，我们重复求平均值的过程，以消除偏差和 获得无偏模板。给出了计算算例，说明了旋度矢量的影响 以及平均变形的方法和我们的施工方法的有效性 无偏模板。 该项目将显著增强我们分析脑图像数据的能力；改善诊断、监测 ，以及治疗脑部疾病和精神障碍。该项目有一个重要的培训和 教育部分。具体来说，一名博士生将参与算法设计、计算机代码编写 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.