Statistical models of sets of curves and surfaces based on currents
Statistical models of sets of curves and surfaces based on currents
复制标题
DOI：
10.1016/j.media.2009.07.007
复制
发表时间：
2009-10-01
影响因子：
10.9
通讯作者：
Ayache, Nicholas
中科院分区：
文献类型：
--
作者：
Durrleman, Stanley;Pennec, Xavier;Ayache, Nicholas
对于从医学图像分析到计算机图形学的许多应用来说，计算、可视化和解释曲线或曲面等形状的统计数据是一个真正的挑战。使用电流对此类几何图元进行建模避免了将图元之间的比较基于几何测量（如长度、面积或曲率）的选择或基于点对应的假设。该框架已被相关地用于记录大脑表面或测量几何不变量。然而，虽然最先进的方法可以有效地执行成对配准，但由于随着数据库规模的增长，复杂性也不断增加，因此需要新的数值方案来处理分组统计。在本文中，我们提出了一种电流匹配追踪算法，它允许我们进行近似。在任何所需的精度下，建模为电流的几何基元群体的平均值和众数。这导致电流的稀疏表示，从而提供了一种可视化的方法。从而解释这些统计数据。更重要的是，该工具使我们能够根据严格的统计模型从当前群体中构建地图集。在该模型中，数据被视为受随机电流扰动的未知模板的变形。最大后验方法用于一致地估计模板、该模板对每个数据的变形以及残余扰动。变形和残余电流的统计数据提供了结构几何变异的完整描述。最终，该框架是通用的，可以应用于大范围的解剖数据。我们通过描述脑沟线、大脑内部结构表面和白质纤维束的群体的变异性来展示我们的方法的相关性。对模拟数据的补充实验显示了该方法在监督学习背景下给出病理解剖特征的潜力。 (C) 2009 Elsevier B.V. 保留所有权利。
Computing, visualizing and interpreting statistics on shapes like curves or surfaces is a real challenge with many applications ranging from medical image analysis to computer graphics. Modeling such geometrical primitives with currents avoids to base the comparison between primitives either on a selection of geometrical measures (like length, area or curvature) or on the assumption of point-correspondence. This framework has been used relevantly to register brain surfaces or to measure geometrical invariants. However, while the state-of-the-art methods efficiently perform pairwise registrations, new numerical schemes are required to process groupwise statistics due to an increasing complexity when the size of the database is growing.In this paper, we propose a Matching Pursuit Algorithm for currents, which allows us to approximate. at any desired accuracy, the mean and modes of a population of geometrical primitives modeled as currents. This leads to a sparse representation of the currents, which offers a way to visualize. and hence to interpret, such statistics. More importantly, this tool allows us to build atlases from a population of currents, based on a rigorous statistical model. In this model, data are seen as deformations of an unknown template perturbed by random currents. A Maximum A Posteriori approach is used to estimate consistently the template, the deformations of this template to each data and the residual perturbations. Statistics on both the deformations and the residual currents provide a complete description of the geometrical variability of the structures.Eventually, this framework is generic and can be applied to a large range of anatomical data. We show the relevance of our approach by describing the variability of population of sulcal lines, surfaces of internal structures of the brain and white matter fiber bundles. Complementary experiments on simulated data show the potential of the method to give anatomical characterization of pathologies in the context of supervised learning. (C) 2009 Elsevier B.V. All rights reserved.