Characterizing volume and surface deformations in an atlas framework: theory, applications, and implementation
Characterizing volume and surface deformations in an atlas framework: theory, applications, and implementation
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DOI：
10.1016/s1053-8119(03)00019-3
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发表时间：
2003-03-01
期刊：
影响因子：
5.7
通讯作者：
Woods, RP
中科院分区：
文献类型：
--
作者：
Woods, RP
给定用于将图像或表面映射到图谱配置中的变形，描述用于表征平均变形和与该平均值的偏差的方法。雅可比矩阵被用来表征局部变形，该方法可以应用于任何图像变形方法，雅可比矩阵可以计算。该方法利用的事实是，每个矩阵描述符的局部变形所需的匹配图像的图集对应于半黎曼流形上的一个点。通过确保均值矩阵位于该流形内，可以保留所有图像共有的基本几何特性。与平均值的局部偏差可以在与平均值处的半黎曼流形相切的欧几里得空间中表征，并且可以跨图谱内的多个采样位置全局地累积，以生成每个图像如何偏离平均值的全局多变量表征。(C)2003 Elsevier Science（美国）。All rights reserved.
Given deformations for mapping images or surfaces into an atlas configuration, methods are described for characterizing the mean deformation and deviations from this mean. Jacobian matrices are used to characterize the deformations locally, and the method can be applied to any image warping method for which Jacobian matrices can be computed. The method makes use of the fact that each matrix descriptor of the local deformation required to match an image to the atlas corresponds to a point on a semi-Riemannian manifold. By assuring that the mean matrix lies within this manifold, fundamental geometric properties common to all of the images can be preserved. Local deviations from the mean can be characterized in a euclidean space tangent to the semi-Riemannian manifold at the mean and can be accumulated globally across multiple sampling locations within the atlas to generate a global multivariate characterization of how each image deviates from the mean. (C) 2003 Elsevier Science (USA). All rights reserved.