Deep neural networks (DNNs) frequently fail to generalize to out-of-distribution (OOD) medical images because of variations in scanners and acquisition protocols. Retraining DNN models to address these distribution shifts is often impractical due to the high cost of acquiring and annotating new medical datasets. To address this, we introduce VarDeepPCA, a novel lightweight variational DNN framework designed to restore/refine degraded segmentation maps by leveraging intrinsic geometric priors. Unlike existing approaches that require target-domain data or extensive pre-training, our VarDeepPCA explicitly learns a distribution of valid anatomical geometries using only small in-distribution (ID) datasets. Theoretically, our novel variational learning framework leverages a reinterpretation of the softmax mapping to implicitly perform exact distribution modeling, thereby enabling computationally efficient, sampling-free learning and inference. This also enables VarDeepPCA to provide uncertainty estimates associated with its restored segmentation maps. We empirically validate our framework across 4 distinct clinical applications, using 14 publicly available datasets, involving segmentation of the myocardium, neuroretinal rim, prostate, and fetal head. Comparisons against 15 existing methods demonstrate that VarDeepPCA consistently restores segmentation maps produced by the existing methods on OOD data to (i) significantly improve anatomical plausibility of geometries and clinical utility of the segmentations, and (ii) significantly reduce errors, without needing any more training data than that used by existing methods.

翻译：深度神经网络（DNN）常因扫描仪和采集协议的差异，难以泛化至分布外（OOD）医学图像。由于获取和标注新医学数据集的成本高昂，重新训练DNN模型以应对这些分布偏移往往不切实际。为解决此问题，我们提出VarDeepPCA——一种新颖的轻量级变分DNN框架，通过利用内在几何先验来恢复/细化降质的分割图。与需要目标域数据或大量预训练的现有方法不同，我们的VarDeepPCA仅使用小规模分布内（ID）数据集，即可显式学习有效解剖几何形状的分布。在理论上，我们新颖的变分学习框架通过对softmax映射的重新解释，隐式执行精确分布建模，从而实现计算高效的无采样学习与推理。这还使VarDeepPCA能够为其恢复的分割图提供不确定性估计。我们通过4种不同的临床应用，使用14个公开数据集（涉及心肌、视神经乳头边缘、前列腺和胎儿头部分割）对框架进行实证验证。与15种现有方法的对比表明，VarDeepPCA能持续恢复这些方法在OOD数据上生成的分割图，从而：（i）显著提升几何形状的解剖合理性和分割的临床实用性；（ii）显著减少误差，且无需比现有方法使用更多的训练数据。