Fishbaugh James, Prastawa Marcel, Gerig Guido, Durrleman Stanley
Inf Process Med Imaging. 2013;23:718-29. doi: 10.1007/978-3-642-38868-2_60.
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.
形状回归正成为用于对随时间变化的形状进行统计分析的重要工具。在本文中，我们通过将简单线性回归扩展到在大变形微分同胚度量映射（LDDMM）框架中表示为流的形状空间，开发了一种描述形状随时间变化的新生成模型。通过与线性回归类比，我们估计一个基线形状（截距）和初始动量（斜率），它们完全参数化测地线形状演化。这与先前假设基线形状固定的形状回归方法形成对比。我们进一步利用控制点公式，它提供了大微分同胚变换的离散且低维参数化。这个灵活的系统将变形的参数化与特定形状表示解耦，允许用户定义变形参数的维度。我们提出一种优化方案，通过单一梯度下降算法同时估计基线形状、控制点位置和初始动量。最后，我们在合成数据以及真实解剖形状复合体上展示了我们提出的方法。
