Parametric Meets Non-parametric: Bridging Dual Prediction Spaces for Semi-supervised Medical Image Segmentation

Semi-supervised medical image segmentation leverages abundant unlabeled data to reduce the reliance on costly dense annotations, yet its dominant pseudo-labeling paradigm suffers from inevitable prediction noise, especially under scarce supervision. In this work, we observe that parametric network predictions and non-parametric prototype-based predictions exhibit complementary behaviors under pseudo-label noise: the former offers high expressiveness in capturing local structures but is sensitive to erroneous supervision, while the latter provides stable semantic guidance by aggregating class-level statistics but may lack spatial precision. Motivated by this observation, we propose a simple yet effective complementary learning framework that jointly exploits the parametric prediction space and the non-parametric prototype space for semi-supervised segmentation. Specifically, we introduce a confidence-aware selection mechanism that identifies reliable voxels from either prediction space, a prototype entropy minimization objective that sharpens the non-parametric semantic anchors, and a dual-space semantic alignment objective that encourages mutual enhancement between the two spaces. The unified objective enables reliability-aware mutual enhancement, where each space guides the other when confident and noisy alignment is suppressed when both are uncertain. Extensive experiments on multiple medical image segmentation benchmarks demonstrate that our method consistently outperforms existing approaches under various label-scarce settings.