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arXiv 1112.3166cs.CVcs.NAmath.NA
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高阶动量分布与局部仿射LDDMM配准

Higher-Order Momentum Distributions and Locally Affine LDDMM Registration

Univ. of Copenhagen(哥本哈根大学);BiomedIQ;INRIA Sophia-Antipolis(法国国家信息与自动化研究所索菲亚·安蒂波利斯中心)

Stefan Sommer, Mads Nielsen, Sune Darkner, Xavier Pennec

AI总结:

本文在LDDMM框架中引入高阶动量分布,通过一阶动量实现局部仿射变换的紧凑表示,从而以极少数参数完成非刚性配准,并直接提供可解释的数学和建模信息。

摘要:

为了实现允许直观分析的稀疏参数化,我们旨在用包含可解释元素的基来表示变形,并希望使用具有描述能力的元素来紧凑地表示变形。为此,本文在LDDMM配准框架中引入了高阶动量分布。先前在LDDMM中使用的零阶动量仅描述局部位移,而本文提出的一阶动量表示一个基,允许局部描述仿射变换,进而紧凑地描述全局非刚性变形中的非平移运动。所得表示从数学和建模角度都包含直接可解释的信息。我们开发了具有高阶动量的配准框架的数学构造,展示了其对稀疏图像配准和变形描述的意义,并提供了参数化如何以极少数参数实现配准的示例。使用高阶动量的参数化的能力和可解释性导致了关节运动的自然建模,该方法有望用于量化阿尔茨海默病期间的心室扩张和进行性萎缩。

英文摘要:

To achieve sparse parametrizations that allows intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the LDDMM registration framework. While the zeroth order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local description of affine transformations and subsequent compact description of non-translational movement in a globally non-rigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction of the registration framework with higher-order momenta, we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters. The capacity and interpretability of the parametrization using higher-order momenta lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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