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

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.

Grab-3D: Detecting AI-Generated Videos from 3D Geometric Temporal Consistency

Recent advances in diffusion-based generation techniques enable AI models to produce highly realistic videos, heightening the need for reliable detection mechanisms. However, existing detection methods provide only limited exploration of the 3D geometric patterns present in generated videos. In this paper, we use vanishing points as an explicit representation of 3D geometry patterns, revealing fundamental discrepancies in geometric consistency between real and AI-generated videos. We introduce Grab-3D, a geometry-aware transformer framework for detecting AI-generated videos based on 3D geometric temporal consistency. To enable reliable evaluation, we construct an AI-generated video dataset of static scenes, allowing stable 3D geometric feature extraction. We propose a geometry-aware transformer equipped with geometric positional encoding, temporal-geometric attention, and an EMA-based geometric classifier head to explicitly inject 3D geometric awareness into temporal modeling. Experiments demonstrate that Grab-3D significantly outperforms state-of-the-art detectors, achieving robust cross-domain generalization to unseen generators.