  Deep learning models have exhibited remarkable efficacy in accurately
delineating the prostate for diagnosis and treatment of prostate diseases, but
challenges persist in achieving robust generalization across different medical
centers. Source-free Domain Adaptation (SFDA) is a promising technique to adapt
deep segmentation models to address privacy and security concerns while
reducing domain shifts between source and target domains. However, recent
literature indicates that the performance of SFDA remains far from satisfactory
due to unpredictable domain gaps. Annotating a few target domain samples is
acceptable, as it can lead to significant performance improvement with a low
annotation cost. Nevertheless, due to extremely limited annotation budgets,
careful consideration is needed in selecting samples for annotation. Inspired
by this, our goal is to develop Active Source-free Domain Adaptation (ASFDA)
for medical image segmentation. Specifically, we propose a novel
Uncertainty-guided Tiered Self-training (UGTST) framework, consisting of
efficient active sample selection via entropy-based primary local peak
filtering to aggregate global uncertainty and diversity-aware redundancy
filter, coupled with a tiered self-learning strategy, achieves stable domain
adaptation. Experimental results on cross-center prostate MRI segmentation
datasets revealed that our method yielded marked advancements, with a mere 5%
annotation, exhibiting an average Dice score enhancement of 9.78% and 7.58% in
two target domains compared with state-of-the-art methods, on par with fully
supervised learning. Code is available at:https://github.com/HiLab-git/UGTST
