Partial-to-Full Registration based on Gradient-SDF for Computer-Assisted Orthopedic Surgery

TL;DR

This work tackles CAOS bone registration when intraoperative data are sparse and partially overlapped by proposing a gradient-SDF representation of the pre-operative bone model and a correspondence-free Gauss-Newton optimization to estimate the rigid transform $X=(\mathbf{R},\mathbf{t})$. A robust IRLS framework with a Cauchy M-estimator down-weights outliers, preventing noise from dominating the registration. The method demonstrates fast convergence (under 1 s) and lower MAE/CD than benchmarks across multi-category bone datasets and phantom tests, maintaining accuracy under substantial noise and up to $90\%$ outliers, with phantom TREs around $2.2$–$2.7$ mm. The approach integrates easily into CAOS workflows by allowing random point probing over bone surfaces without landmark correspondence, offering practical time savings and clinical value.

Abstract

In computer-assisted orthopedic surgery (CAOS), accurate pre-operative to intra-operative bone registration is an essential and critical requirement for providing navigational guidance. This registration process is challenging since the intra-operative 3D points are sparse, only partially overlapped with the pre-operative model, and disturbed by noise and outliers. The commonly used method in current state-of-the-art orthopedic robotic system is bony landmarks based registration, but it is very time-consuming for the surgeons. To address these issues, we propose a novel partial-to-full registration framework based on gradient-SDF for CAOS. The simulation experiments using bone models from publicly available datasets and the phantom experiments performed under both optical tracking and electromagnetic tracking systems demonstrate that the proposed method can provide more accurate results than standard benchmarks and be robust to 90% outliers. Importantly, our method achieves convergence in less than 1 second in real scenarios and mean target registration error values as low as 2.198 mm for the entire bone model. Finally, it only requires random acquisition of points for registration by moving a surgical probe over the bone surface without correspondence with any specific bony landmarks, thus showing significant potential clinical value.

Figures (5)

• Figure 1: Registration pattern for pelvis and femur in MAKO lonner2019robotics. The dots show the bony landmarks to be accurately verified and acquired by the probe for registration.
• Figure 2: Our framework: the pre-operative model is represented as gradient-SDF which is a hybrid representation between standard SDF stored in a voxel grid and explicit geometry representation using surfels (surface normal). The intra-operative points are collected by moving the probe over the bone surface.
• Figure 3: The parts circled in red dotted lines are bone structures that may be exposed during orthopaedic surgeries. In order from left to right: pelvic acetabulum; proximal femur; femoral condyle; proximal tibia. The yellow points are the simulated surgical probe picking points, which are used as partial data to be registered with the full point cloud model.
• Figure 4: Setups: repeated trials were performed with the sawbones models in each of the two tracking systems. Points were collected by moving the probe over the pelvic acetabulum and proximal femur.
• Figure 5: Two examples of the real data from phantom experiments.