Principal component based diffeomorphic surface mapping.
Principal component based diffeomorphic surface mapping.
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DOI：
10.1109/tmi.2011.2168567
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发表时间：
2012-02
影响因子：
10.6
通讯作者：
Miller MI
中科院分区：
文献类型：
--
作者：
Qiu A;Younes L;Miller MI
提出了一种新的基于大变形几何纯度量映射（LDDMM）的几何纯曲面映射算法。与现有的LDDMM方法不同，这种新算法通过将形状先验（其中，非线性非纯形状空间由来自固定模板的非纯测地线流的初始动量的线性空间表示）结合在一起来降低非纯变换估计的复杂性。此外，第一次，在决策理论方案的基础上贝叶斯建模，其中的经验形状先验的特点是由一个低维高斯分布的初始动量内制定的同构映射。这是使用主成分分析（PCA）来构建初始动量的本征空间。一个似然函数被制定为观察表面的条件概率给定的任何特定值的初始动量，这是建模为一个随机场的向量值的测量表征的几何表面。我们将微分同胚映射定义为在初始动量本征空间上给定可观察表面的情况下最大化初始动量后验分布的问题。我们证明了初始动量特征空间的稳定性时，使用自举方法改变训练样本。然后，我们验证映射的准确性，并显示出鲁棒性的形状变化不纳入形状先验的离群值。
We present a new diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping (LDDMM). Unlike existing LDDMM approaches, this new algorithm reduces the complexity of the estimation of diffeomorphic transformations by incorporating a shape prior in which a nonlinear diffeomorphic shape space is represented by a linear space of initial momenta of diffeomorphic geodesic flows from a fixed template. In addition, for the first time, the diffeomorphic mapping is formulated within a decision-theoretic scheme based on Bayesian modeling in which an empirical shape prior is characterized by a low dimensional Gaussian distribution on initial momentum. This is achieved using principal component analysis (PCA) to construct the eigenspace of the initial momentum. A likelihood function is formulated as the conditional probability of observing surfaces given any particular value of the initial momentum, which is modeled as a random field of vector-valued measures characterizing the geometry of surfaces. We define the diffeomorphic mapping as a problem that maximizes a posterior distribution of the initial momentum given observable surfaces over the eigenspace of the initial momentum. We demonstrate the stability of the initial momentum eigenspace when altering training samples using a bootstrapping method. We then validate the mapping accuracy and show robustness to outliers whose shape variation is not incorporated into the shape prior.