HadBalance: A Plug-and-Play Unified Global Geometric Prior Framework for Generalizable Biomedical Segmentation
Authors: Zhuangzhi Gao, Feixiang Zhou, He Zhao, Wenhan Chen, Ruiyu Luo, Xin Wang, Hongyi Qin, Zhongli Wu, +6 more
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.
Convexity is a fundamental geometric prior that underlies many natural and man-made structures, yet remains challenging to impose effectively in end-to-end trainable segmentation networks. We revisit convexity from a functional perspective and propose a unified, threshold-free convexity prior based on the quasi-concavity of the network's output mask function u. Instead of constraining a single binary segmentation, we require all super-level sets of u to be convex, transforming global shape constraints into local, differentiable inequalities on u and its derivatives. From this principle, we derive zero, first, and second-order characterizations, yielding respectively a local midpoint convexification algorithm, a gradient-based condition linked to supporting hyperplanes, and a sufficient second-order inequality expressed as a quadratic form on the tangent plane. The first and second-order formulations produce a compact convolutional loss that can be densely applied across the image without thresholding. Our quasi-concavity losses integrate seamlessly with modern segmentation networks via the proposed convex gradient projection module (CGPM). They consistently enforce convexity and improve shape regularity across multiple datasets, outperforming networks tailored for retinal segmentation and surpassing previous shape-aware methods. Remarkably, our analysis unifies a wide spectrum of previous convex shape models, from discrete 1-0-1 line constraints and graph-cuts convexity formulations to curvature or signed distance Laplacian based level-set priors, within a single continuous and differentiable framework.
Medical image classification models are ideally expected to identify diagnostically relevant regions while making predictions, yet standard classification losses rarely provide spatial supervision. Explicit supervision via anatomical shape information, such as segmentation masks of task-relevant anatomy, has been shown to guide the network toward regions relevant to the target prediction. However, obtaining such masks incurs substantial manual annotation effort and computational overhead. With the advent of segmentation foundation models that exhibit strong localization of anatomical structures across diverse imaging modalities, we leverage this capability to extract anatomical shape priors without the burden of training a dedicated segmentation model. In this paper, we propose a new framework, Locus, an anatomical attention regularization framework that leverages pretrained segmentation foundation models to guide a classifier's attention toward diagnostically meaningful anatomical structures across diverse imaging modalities. Instead of enforcing pixel-wise alignment with the foundation-model-derived mask, we introduce a regularization term that adaptively balances attention between anatomical (foreground) and background regions, penalizing the classifier when background attention dominates. We validate Locus on eight diverse medical imaging datasets spanning dermoscopy, X-ray, histopathology, and cardiac MRI, showing consistent gains in classification performance alongside improved anatomically grounded attention.
Whole-heart multi-compartment CT segmentation is clinically important, but standard CNNs do not explicitly enforce anatomical plausibility. Based on statistics derived from the training data, we evaluate whether lightweight explicit shape priors, implemented as shape-aware losses and spatial label distribution heatmap-guided U-Net variants, improve 3D cardiac segmentation on MM-WHS CT and WHS++. Across all experiments, a standard 3D U-Net surprisingly remained a very strong baseline, with handcrafted priors yielding at best marginal and inconsistent changes and often degrading performance. These results suggest that the baseline already captures substantial implicit anatomical regularities and that future gains will likely require more expressive learned priors rather than simple handcrafted anatomical shape constraints.