Durrleman Stanley, Pennec Xavier, Trouvé Alain, Ayache Nicholas
Asclepios Team Project, INRIA Sophia Antipolis, Méditerranée, 2004 Route des Lucioles, 06902 Sophia Antipolis Cedex, France.
Med Image Anal. 2009 Oct;13(5):793-808. doi: 10.1016/j.media.2009.07.007. Epub 2009 Jul 17.
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.
对曲线或曲面等形状进行统计计算、可视化和解释是一项真正的挑战，其应用范围广泛，涵盖从医学图像分析到计算机图形学等诸多领域。用流来对这些几何基元进行建模，避免了基于几何度量的选择（如长度、面积或曲率）或点对应假设来进行基元之间的比较。这个框架已被相关地用于配准脑表面或测量几何不变量。然而，尽管当前的先进方法能够高效地执行成对配准，但由于数据库规模不断增大时复杂度的增加，需要新的数值方案来处理成组统计。在本文中，我们提出了一种针对流的匹配追踪算法，它使我们能够以任何期望的精度逼近建模为流的一组几何基元的均值和众数。这导致了流的稀疏表示，为可视化并进而解释此类统计提供了一种方法。更重要的是，这个工具使我们能够基于严格的统计模型从一组流构建图谱。在这个模型中，数据被视为由随机流扰动的未知模板的变形。采用最大后验方法来一致地估计模板、该模板到每个数据的变形以及残余扰动。对变形和残余流的统计提供了结构几何变异性的完整描述。最终，这个框架具有通用性，可应用于大量的解剖数据。我们通过描述脑沟线群体、脑内部结构表面和白质纤维束的变异性来展示我们方法的相关性。在模拟数据上的补充实验表明了该方法在监督学习背景下对病变进行解剖特征描述的潜力。
