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计算解剖学流形的统计计算

Statistical Computing on Manifolds for Computational Anatomy
课程网址: http://videolectures.net/etvc08_pennec_scomf/  
主讲教师: Xavier Pennec
开课单位: 法国国家信息与自动化研究所
开课时间: 2008-11-05
课程语种: 英语
中文简介:
计算解剖学是一门新兴学科，旨在分析和模拟器官的个体解剖结构及其在人群中的生物变异性。目标不仅是对群体中的正常变异进行建模，还要发现正常和病理群体之间的形态差异，并可能从结构异常中检测，建模和分类病理。应用在神经科学，最小化功能组分析中的解剖变异性影响以及医学成像中非常重要，以更好地推动解剖学（图谱）的通用模型适应患者特定数据。然而，理解和建模器官的形状是由di？缺乏用于比较不同主题的物理模型，形状的复杂性以及隐含的高自由度。此外，通常提取的解剖特征的几何特性提出了对不属于标准欧几里德空间的曲线，曲面和变形等对象的统计和计算方法的需求。我们在本章中研究黎曼度量作为开发通用算法以计算流形的基础。我们表明，很少有计算工具推导出这种结构可以在实践中用作构建更复杂的通用算法的基本原子，如平均计算，马哈拉诺比斯距离，插值，过滤和几何特征领域的各向异性扩散。这个计算框架通过分析脊柱侧凸的形状和脑沟线的大脑变异模型来说明，结果表明新的解剖学结果。
课程简介: Computational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. The goal is not only to model the normal variations among a population, but also discover morphological diferences between normal and pathological populations, and possibly to detect, model and classify the pathologies from structural abnormalities. Applications are very important both in neuroscience, to minimize the inuence of the anatomical variability in functional group analysis, and in medical imaging, to better drive the adaptation of generic models of the anatomy (atlas) into patient-specic data. However, understanding and modeling the shape of organs is made di- cult by the absence of physical models for comparing diferent subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics and computational methods on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We investigate in this chapter the Riemannian metric as a basis for developing generic algorithms to compute on manifolds. We show that few computational tools derive this structure can be used in practice as the basic atoms to build more complex generic algorithms such as mean computation, Mahalanobis distance, interpolation, ltering and anisotropic difusion on elds of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings.
关 键 词: 计算解剖学; 病理群体; 形态差异
课程来源: 视频讲座网
最后编审: 2019-04-13：cwx
阅读次数: 86

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