Topology‐Aware AR With G3‐Depth for Minimally Invasive Surgery

ABSTRACT This study proposes a topology‐aware 3D augmented reality (AR) framework for minimally invasive surgery (MIS) and robot‐assisted MIS (RAMIS) to address the limited field of view and lack of depth perception in 2D endoscopic imaging. Central to the framework is a novel self‐supervised depth estimation method, ‐, which employs a translation‐to‐permutation encoder with group equivariance and four‐connectivity graph structures to capture non‐Euclidean geometric features and generate accurate 3D point clouds, particularly for surgical instruments. The reconstructed depth maps enable real‐time AR overlays, Poisson surface‐based mesh reconstruction, and precise instrument–organ distance measurement. Extensive evaluation on DaVinci, SCARED, SERV‐CT, and Hamlyn heart datasets demonstrates significant performance improvements over state‐of‐the‐art methods, with Abs Rel gains of approximately and . Validation in multiple surgical scenarios confirms enhanced depth perception and reliable spatial awareness, highlighting the framework's potential to improve surgical precision, safety, and clinical outcomes.