PinPoint: Monocular Needle Pose Estimation for Robotic Suturing via Stein Variational Newton and Geometric Residuals

Reliable estimation of surgical needle 3D position and orientation is essential for autonomous robotic suturing, yet existing methods operate almost exclusively under stereoscopic vision. In monocular endoscopic settings, common in transendoscopic and intraluminal procedures, depth ambiguity and rotational symmetry render needle pose estimation inherently ill-posed, producing a multimodal distribution over feasible configurations, rather than a single, well-grounded estimate. We present PinPoint, a probabilistic variational inference framework that treats this ambiguity directly, maintaining a distribution of pose hypotheses rather than suppressing it. PinPoint combines monocular image observations with robot-grasp constraints through analytical geometric likelihoods with closed-form Jacobians. This framework enables efficient Gauss-Newton preconditioning in a Stein Variational Newton inference, where second-order particle transport deterministically moves particles toward high-probability regions while kernel-based repulsion preserves diversity in the multimodal structure. On real needle-tracking sequences, PinPoint reduces mean translational error by 80% (down to 1.00 mm) and rotational error by 78% (down to 13.80°) relative to a particle-filter baseline, with substantially better-calibrated uncertainty. On induced-rotation sequences, where monocular ambiguity is most severe, PinPoint maintains a bimodal posterior 84% of the time, almost three times the rate of the particle filter baseline, correctly preserving the alternative hypothesis rather than committing prematurely to one mode. Suturing experiments in ex vivo tissue demonstrate stable tracking through intermittent occlusion, with average errors during occlusion of 1.34 mm in translation and 19.18° in rotation, even when the needle is fully embedded.