PDSC: a dynamic stopping criterion for active learning in medical image segmentation: a multi-dataset evaluation

Active learning (AL) reduces annotation costs in medical image segmentation by iteratively selecting informative samples for labelling. However, a critical yet often overlooked challenge is determining when to stop training during each AL iteration. Conventional stopping strategies, such as fixed-epoch schedules or early stopping, often rely on prior knowledge of full datasets for tuning or exploratory training runs, assuming stable and representative data distributions. These assumptions break down as the labelled set evolves across AL rounds, creating design bias and limiting generalisability in real-world AL scenarios. To address this, we introduce a novel Chebyshev Polynomial-based Dynamic Stopping Criterion (PDSC) that detects training convergence by fitting a Chebyshev polynomial to the validation loss and monitoring the behaviour of its smoothed gradient. Training stops when the percentage change in the fitted curve remains below a threshold for a set number of epochs. Unlike traditional strategies, PDSC dynamically adapts to training using only the currently available labelled data. PDSCs hyperparameters are tuned once in the first AL iteration using only this initial labelled dataset and held fixed thereafter, eliminating the need for repeated tuning or reliance on full-dataset trends. We evaluated PDSC on three 3D Medical Segmentation Decathlon tasks (spleen, liver and lung) using a 3D UNet within a pool-based AL framework, comparing against fixed-epoch and early stopping. PDSC consistently matched or outperformed the conventional strategies while substantially reducing training time by up to 80%. PDSC mitigates premature termination from early stopping and limited unnecessary overtraining from fixed schedules, yielding improved stability, generalisation, and robustness under the non-i.i.d., dynamically changing conditions characteristic of AL workflows. PDSC provides a framework for adaptive, stable, and reproducible training control, making it suitable for a wide range of machine-learning workflows, particularly those involving evolving or limited labelled data.