Geodesic shape regression in the framework of currents.
Geodesic shape regression in the framework of currents.
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DOI：
10.1007/978-3-642-38868-2_60
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发表时间：
2013
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影响因子：
--
通讯作者：
Durrleman, Stanley
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文献类型：
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作者：
Fishbaugh, James;Prastawa, Marcel;Gerig, Guido;Durrleman, Stanley
形状回归是一个重要的工具，统计分析的时间依赖的形状。在本文中，我们开发了一个新的生成模型，描述形状随时间的变化，通过扩展简单的线性回归空间的形状表示为电流的大变形几何度量映射（LDDMM）框架。类比线性回归，我们估计基线形状（截距）和初始动量（斜率），完全参数化的测地线形状的演变。这与先前的形状回归方法相反，该方法假设基线形状是固定的。我们进一步利用控制点公式，它提供了大型微分同胚变换的离散和低维参数化。这个灵活的系统将变形的参数化从特定的形状表示中分离出来，允许用户定义变形参数的维度。我们提出了一个优化方案，估计基线形状，控制点的位置，并通过一个单一的梯度下降算法同时初始动量。最后，我们证明了我们提出的方法合成数据以及真实的解剖形状复杂。
Shape regression is emerging as an important tool for the statistical analysis of time dependent shapes. In this paper, we develop a new generative model which describes shape change over time, by extending simple linear regression to the space of shapes represented as currents in the large deformation diffeomorphic metric mapping (LDDMM) framework. By analogy with linear regression, we estimate a baseline shape (intercept) and initial momenta (slope) which fully parameterize the geodesic shape evolution. This is in contrast to previous shape regression methods which assume the baseline shape is fixed. We further leverage a control point formulation, which provides a discrete and low dimensional parameterization of large diffeomorphic transformations. This flexible system decouples the parameterization of deformations from the specific shape representation, allowing the user to define the dimensionality of the deformation parameters. We present an optimization scheme that estimates the baseline shape, location of the control points, and initial momenta simultaneously via a single gradient descent algorithm. Finally, we demonstrate our proposed method on synthetic data as well as real anatomical shape complexes.