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

arXiv: https://arxiv.org/abs/2606.15976 · HTML: https://mlsanity.com/paper/2606.15976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Deep Learning for Medical Image Analysis](https://mlsanity.com/paper/1708.08987/) (2017)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [MSRF-Net: A Multi-Scale Residual Fusion Network for Biomedical Image Segmentation](https://mlsanity.com/paper/2105.07451/) (2021)
- [Fair Resource Allocation in Multi-Task Learning](https://mlsanity.com/paper/2402.15638/) (2024)
- [Robust T-Loss for Medical Image Segmentation](https://mlsanity.com/paper/2306.00753/) (2023)
- [Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation](https://mlsanity.com/paper/2005.07476/) (2020)
- [GLCP: Global-to-Local Connectivity Preservation for Tubular Structure Segmentation](https://mlsanity.com/paper/2507.21328/) (2025)
- [FCB-SwinV2 Transformer for Polyp Segmentation](https://mlsanity.com/paper/2302.01027/) (2023)
- [Convexity Shape Constraints for Image Segmentation](https://mlsanity.com/paper/1509.02122/) (2015)
- [Mixture-of-Shape-Experts (MoSE): End-to-End Shape Dictionary Framework to Prompt SAM for Generalizable Medical Segmentation](https://mlsanity.com/paper/2504.09601/) (2025)
- [Leveraging Persistence Image to Enhance Robustness and Performance in Curvilinear Structure Segmentation](https://mlsanity.com/paper/2601.18045/) (2026)

## Abstract (arXiv)

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.