Real-Time Deformable Registration for Robotic Ultrasound Surgical Guidance Based on Vectorized Trust-Region Optimization

Robotic ultrasound (US)-guided surgery is a common clinical workflow for the diagnosis and treatment of many diseases. Tissue deformation is an important factor that affects surgical accuracy. Intraoperative real-time deformable registration is therefore critical to ensure surgical precision. In this study, a real-time US image nonrigid registration method was proposed. First, the analytical derivatives and corresponding cascaded convolution operations were derived, facilitating the fast calculation of the deformation field and gradients. Second, an optimizer fusing the trust-region and limited-memory Broyden-Fletcher–Goldfarb-Shanno (L-BFGS) method was proposed, which accelerates the optimization by adopting vectorized operations instead of large-scale matrix multiplication. The proposed method achieved real-time nonrigid registration with an average registration time of 30 ms for 2-D images with a resolution of
$256^{2}$
and 500 ms for 3-D images with a resolution of
$112^{3}$
, respectively, on a desktop CPU computing platform. It satisfied clinical real-time requirements without prior dataset construction and training process. The proposed method was validated on public datasets, clinical cases, and robotic phantom intervention experiments. Results demonstrated that our method realized great performance in both registration speed and accuracy. This method is expected to improve the US guidance accuracy of robots, promoting the precision and automation of related surgeries.