Statistical shape modeling (SSM) enables population-based quantitative analysis of anatomical shapes, informing clinical diagnosis. Deep learning approaches predict correspondence-based SSM directly from unsegmented 3D images but require calibrated uncertainty quantification, motivating Bayesian formulations. Variational information bottleneck DeepSSM (VIB-DeepSSM) is an effective, principled framework for predicting probabilistic shapes of anatomy from images with aleatoric uncertainty quantification. However, VIB is only half-Bayesian and lacks epistemic uncertainty inference. We derive a fully Bayesian VIB formulation from both the probably approximately correct (PAC)-Bayes and variational inference perspectives. We demonstrate the efficacy of two scalable approaches for Bayesian VIB with epistemic uncertainty: concrete dropout and batch ensemble. Additionally, we introduce a novel combination of the two that further enhances uncertainty calibration via multimodal marginalization. Experiments on synthetic shapes and left atrium data demonstrate that the fully Bayesian VIB network predicts SSM from images with improved uncertainty reasoning without sacrificing accuracy.

翻译：统计形状建模（SSM）可对解剖结构进行基于群体的定量分析，为临床诊断提供依据。深度学习方法可直接从非分割的三维图像中预测基于对应点的SSM，但需要校准的不确定性量化，这推动了贝叶斯形式的提出。变分信息瓶颈DeepSSM（VIB-DeepSSM）是一种有效且原理性的框架，可通过偶然不确定性量化从图像中预测解剖结构的概率形状。然而，VIB仅为半贝叶斯方法，缺乏认知不确定性推断。我们从概率近似正确（PAC）贝叶斯和变分推断两个角度推导了全贝叶斯VIB形式。我们展示了两种引入认知不确定性的可扩展贝叶斯VIB方法的有效性：具体丢弃法和批量集成法。此外，我们创新性地将两者结合，通过多模态边缘化进一步增强了不确定性校准。在合成形状和左心房数据上的实验表明，全贝叶斯VIB网络在不牺牲精度的前提下，可从图像中预测SSM并提升不确定性推理能力。