HadBalance: A Plug-and-Play Unified Global Geometric Prior Framework for Generalizable Biomedical Segmentation

2026-06-14

AI Summary

Current medical image segmentation methods lack a unified geometric prior capable of generalizing across organs and imaging modalities, often failing to simultaneously preserve structural consistency and fine anatomical details. This work proposes HadBalance, the first plug-and-play framework that introduces a unified geometric prior grounded in the near-convex shape assumption. Leveraging the Hadwiger theorem, it formulates global geometric constraints based on area, perimeter, and Euler characteristic, and incorporates a conflict-aware objective balancing mechanism to adaptively fuse geometric priors with task-specific gradients. Evaluated across diverse organs and imaging modalities, HadBalance significantly improves segmentation accuracy while avoiding over-regularization, effectively enhancing both structural coherence and fidelity to anatomical detail.

Abstract

Precise biomedical image segmentation is crucial for clinical diagnosis. Geometric cues (e.g., boundary, shape, and topology) can improve structural consistency, yet most are task-specific and lack a unified geometric foundation that generalizes across organs and modalities. We are motivated by the observation that several medical segmentation targets can be approximated as globally near-convex shapes. A convex region is one in which any two interior points can be connected by a line segment entirely contained within the region. In practice, medical targets may exhibit small local concavities or boundary irregularities; we refer to such globally convex-like shapes as near-convex. Motivated by this, we derive Hadwiger Shape Priors from Hadwiger's theorem as an interpretable global regularizer using three 2D measures: area A, perimeter P, and Euler characteristic chi, enabling transfer across organs and modalities. However, because medical datasets are shape-heterogeneous, enforcing near-convex priors uniformly can over-regularize non-convex anatomy with significant concavities, washing out concavities and fine details and degrading segmentation accuracy. To address this challenge, we propose Conflict-Aware Objective Balancing (CAOB), which integrates shape priors with segmentation in a gradient-aware manner. For each prior, CAOB removes only the gradient component that conflicts with segmentation while preserving the remaining aligned component, and adaptively regulates objective influences to prevent prior dominance. This enables stable use of shape priors on shape-heterogeneous data without erasing genuine concavities or fine structural details. We call this plug-and-play framework HadBalance.

Problem

• biomedical segmentation
• geometric prior
• near-convex shape
• shape heterogeneity
• over-regularization

Innovation

• Hadwiger Shape Priors
• near-convex
• Conflict-Aware Objective Balancing
• geometric prior
• generalizable segmentation