Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using lower-dimensional shape features, on which statistical analysis can be performed. Various methods for constructing compact shape representations have been proposed, but they involve laborious and costly steps. We propose Image2SSM, a novel deep-learning-based approach for SSM that leverages image-segmentation pairs to learn a radial-basis-function (RBF)-based representation of shapes directly from images. This RBF-based shape representation offers a rich self-supervised signal for the network to estimate a continuous, yet compact representation of the underlying surface that can adapt to complex geometries in a data-driven manner. Image2SSM can characterize populations of biological structures of interest by constructing statistical landmark-based shape models of ensembles of anatomical shapes while requiring minimal parameter tuning and no user assistance. Once trained, Image2SSM can be used to infer low-dimensional shape representations from new unsegmented images, paving the way toward scalable approaches for SSM, especially when dealing with large cohorts. Experiments on synthetic and real datasets show the efficacy of the proposed method compared to the state-of-art correspondence-based method for SSM.

翻译：统计形状建模（SSM）是分析解剖形态变化的重要工具。在典型的SSM流程中，经过分割和刚性配准的三维解剖图像通过低维形状特征进行表征，从而可对其进行统计分析。目前已有多种构建紧凑形状表示的方法被提出，但这些方法涉及繁琐且成本高昂的步骤。我们提出Image2SSM——一种基于深度学习的新型SSM方法，利用图像-分割对直接从图像中学习基于径向基函数（RBF）的形状表示。这种基于RBF的形状表示为网络提供了丰富的自监督信号，使其能够以数据驱动的方式估算底层曲面的连续且紧凑表示，从而适应复杂几何结构。Image2SSM可通过构建基于统计地标的形状模型来描述感兴趣的生物结构群体，且无需最小化参数调优及用户辅助。训练完成后，Image2SSM可用于从新的未分割图像中推断低维形状表示，为SSM的可扩展方法（尤其在处理大规模数据队列时）铺平道路。在合成数据集和真实数据集上的实验表明，与当前最先进的基于对应点的方法相比，所提方法在SSM中具有显著有效性。