Vicinal Feature Statistics Augmentation for Federated 3D Medical Volume Segmentation

Federated learning (FL) enables multiple client medical institutes collaboratively train a deep learning (DL) model with privacy protection. However, the performance of FL can be constrained by the limited availability of labeled data in small institutes and the heterogeneous (i.e., non-i.i.d.) data distribution across institutes. Though data augmentation has been a proven technique to boost the generalization capabilities of conventional centralized DL as a "free lunch", its application in FL is largely underexplored. Notably, constrained by costly labeling, 3D medical segmentation generally relies on data augmentation. In this work, we aim to develop a vicinal feature-level data augmentation (VFDA) scheme to efficiently alleviate the local feature shift and facilitate collaborative training for privacy-aware FL segmentation. We take both the inner- and inter-institute divergence into consideration, without the need for cross-institute transfer of raw data or their mixup. Specifically, we exploit the batch-wise feature statistics (e.g., mean and standard deviation) in each institute to abstractly represent the discrepancy of data, and model each feature statistic probabilistically via a Gaussian prototype, with the mean corresponding to the original statistic and the variance quantifying the augmentation scope. From the vicinal risk minimization perspective, novel feature statistics can be drawn from the Gaussian distribution to fulfill augmentation. The variance is explicitly derived by the data bias in each individual institute and the underlying feature statistics characterized by all participating institutes. The added-on VFDA consistently yielded marked improvements over six advanced FL methods on both 3D brain tumor and cardiac segmentation.