FedBSE: Federated Bayesian State Evolution for Open-Client Medical Image Segmentation

Federated medical image segmentation enables collaborative learning across multiple institutions without sharing raw patient data. However, most existing methods assume a fixed set of participating clients before training, which does not reflect real-world medical collaboration networks where new institutions may continue to join after deployment. Restarting federated training introduces additional communication and optimization costs, while updating the shared model may degrade performance on existing clients. To address this issue, we propose FedBSE, a federated Bayesian state evolution framework for medical image segmentation with open client participation. FedBSE explicitly separates shared segmentation knowledge from client-specific variations and freezes the shared components after the initial federated training stage. For each newly arriving client, the method uses local labeled data and the current state prior to derive a closed-form estimate in a low-dimensional client-state space. This avoids iterative optimization of the full segmentation network and keeps the predictors of existing clients unchanged. The inferred client state and its local posterior uncertainty are then adopted to update the server-maintained state distribution through Gaussian moment matching. The updated distribution serves as the prior for subsequent clients. Experiments on three public multi-center medical image segmentation datasets show that FedBSE achieves competitive segmentation performance while substantially reducing new-client onboarding costs. It also enables the client-state distribution to evolve continuously as new clients arrive.