arg-VU: Affordance Reasoning with Physics-Aware 3D Geometry for Visual Understanding in Robotic Surgery

Affordance reasoning provides a principled link between perception and action, yet remains underexplored in surgical robotics, where tissues are highly deformable, compliant, and dynamically coupled with tool motion. We present arg-VU, a physics-aware affordance reasoning framework that integrates temporally consistent geometry tracking with constraint-induced mechanical modeling for surgical visual understanding. Surgical scenes are reconstructed using 3D Gaussian Splatting (3DGS) and converted into a temporally tracked surface representation. Extended Position-Based Dynamics (XPBD) embeds local deformation constraints and produces representative geometry points (RGPs) whose constraint sensitivities define anisotropic stiffness metrics capturing the local constraint-manifold geometry. Robotic tool poses in SE(3) are incorporated to compute rigidly induced displacements at RGPs, from which we derive two complementary measures: a physics-aware compliance energy that evaluates mechanical feasibility with respect to local deformation constraints, and a positional agreement score that captures motion alignment (as kinematic motion baseline). Experiments on surgical video datasets show that arg-VU yields more stable, physically consistent, and interpretable affordance predictions than kinematic baselines. These results demonstrate that physics-aware geometric representations enable reliable affordance reasoning for deformable surgical environments and support embodied robotic interaction.