Pareto-Guided Optimization for Uncertainty-Aware Medical Image Segmentation

TL;DR

This work tackles non-uniform uncertainty in medical image segmentation by prioritizing region-wise learning, especially around uncertain boundaries. It introduces Intuitionistic Fuzzy Labels to softly represent boundary ambiguity and a Pareto-consistent fuzzy auxiliary loss to reshape the optimization landscape, with two learnable scalars $\\rho_1$ and $\\rho_2$ that adaptively balance boundary and interior regions. A region-wise curriculum strategy progressively shifts from interior-focused learning to boundary-aware refinement, realized through continuous Pareto dynamics that interpolate between the Dice loss and fuzzy regularization as training progresses. Empirical results on BraTS18 and Pretreat-MetsToBrain-Masks demonstrate improved Dice scores and markedly better training stability across full, single, and missing modalities, supported by ablations and parameter-dynamics analyses. The proposed framework offers robust, uncertainty-aware segmentation suitable for clinical scenarios with incomplete data or annotation variability.

Abstract

Uncertainty in medical image segmentation is inherently non-uniform, with boundary regions exhibiting substantially higher ambiguity than interior areas. Conventional training treats all pixels equally, leading to unstable optimization during early epochs when predictions are unreliable. We argue that this instability hinders convergence toward Pareto-optimal solutions and propose a region-wise curriculum strategy that prioritizes learning from certain regions and gradually incorporates uncertain ones, reducing gradient variance. Methodologically, we introduce a Pareto-consistent loss that balances trade-offs between regional uncertainties by adaptively reshaping the loss landscape and constraining convergence dynamics between interior and boundary regions; this guides the model toward Pareto-approximate solutions. To address boundary ambiguity, we further develop a fuzzy labeling mechanism that maintains binary confidence in non-boundary areas while enabling smooth transitions near boundaries, stabilizing gradients, and expanding flat regions in the loss surface. Experiments on brain metastasis and non-metastatic tumor segmentation show consistent improvements across multiple configurations, with our method outperforming traditional crisp-set approaches in all tumor subregions.

Figures (10)

• Figure 1: The proposed region-aware segmentation framework that tackles boundary ambiguity and slice-wise inconsistencies through (a) label ambiguity and label inconsistency between adjacent slices, (b) model output and uncertainty map, and (c) a region-wise curriculum learning approach with intuitionistic fuzzy labels to stabilise training and improve segmentation accuracy.
• Figure 2: Qualitative visualization of segmentation results on mmformer with BraTS18 dataset. Model Prediction is mmformer + fuzzy, Baseline Prediction is mmformer.
• Figure 3: Training Stability Analysis on mmFormer under the missing modalities
• Figure 4: Evolution of the learnable fuzzy parameters $\rho_1$ and $\rho_2$ during training. Consistent with the gradient analysis in Sec. \ref{['sec:rho_analysis']}, $\rho_1$ monotonically increases towards $1^-$, indicating growing confidence in the logits-based membership, while $\rho_2$ asymptotically decays towards $0^+$, gradually annealing the regularization from the non-membership term.
• Figure 5: Cosine similarity between our IFL and other losses during training.