SurgURDF-Calib: Learning Robust Geometric Optimization for Surgical Robot Camera Calibration

Camera-robot extrinsic calibration is essential for aligning surgical robot kinematics with endoscopic observations, yet remains challenging under specular appearance, articulated motion, occlusion, and partial visibility. We introduce SurgURDF-Calib, a geometry-structured learned optimization framework that preserves an analytical SE(3) solver rather than directly regressing camera extrinsics. Given a surgical video, robot joint states, URDF geometry, and an initial extrinsic estimate, we first construct a compact optimization candidate pool using motion diversity and instrument visibility. A learned coarse calibration module then predicts a sequence-level correction to move the estimate into a favorable convergence basin. Starting from this initialization, the second stage performs geometry-guided refinement through observability-aware D-optimal frame scheduling and a learned robust sparse Levenberg-Marquardt (LM) solver, which adaptively estimates geometric factor weights and anisotropic damping while retaining analytical pose updates. We further introduce SurgURDF-100K, a geometry-consistent benchmark containing 1,000 surgical sequences and 100K annotated observations. Experiments on synthetic and real surgical videos demonstrate improved calibration accuracy and robustness under challenging initialization and unreliable observations, together with generalization to unseen instrument geometries.