SurgCalib: Gaussian Splatting-Based Hand-Eye Calibration for Robot-Assisted Minimally Invasive Surgery

TL;DR

This paper introduces SurgCalib, a markerless, Gaussian Splatting-based framework for accurate hand-eye calibration in robot-assisted minimally invasive surgery, addressing challenges of cable-driven robots and avoiding OR disruptions.

Contribution

SurgCalib is a novel, automatic, markerless calibration method that refines instrument pose using a differentiable rendering pipeline under RCM constraints.

Findings

Achieved average 2D tool-tip reprojection errors of around 12 pixels.

Attained 3D tool-tip Euclidean errors below 6 mm.

Validated on the SurgPose benchmark with promising accuracy.

Abstract

We present a Gaussian Splatting-based framework for hand-eye calibration of the da Vinci surgical robot. In a vision-guided robotic system, accurate estimation of the rigid transformation between the robot base and the camera frame is essential for reliable closed-loop control. For cable-driven surgical robots, this task faces unique challenges. The encoders of surgical instruments often produce inaccurate proprioceptive measurements due to cable stretch and backlash. Conventional hand-eye calibration approaches typically rely on known fiducial patterns and solve the AX = XB formulation. While effective, introducing additional markers into the operating room (OR) environment can violate sterility protocols and disrupt surgical workflows. In this study, we propose SurgCalib, an automatic, markerless framework that has the potential to be used in the OR. SurgCalib first initializes the pose of the surgical instrument using raw kinematic measurements and subsequently refines this pose through a two-phase optimization procedure under the RCM constraint within a Gaussian Splatting-based differentiable rendering pipeline. We evaluate the proposed method on the public dVRK benchmark, SurgPose. The results demonstrate average 2D tool-tip reprojection errors of 12.24 px (2.06 mm) and 11.33 px (1.9 mm), and 3D tool-tip Euclidean distance errors of 5.98 mm and 4.75 mm, for the left and right instruments, respectively.