2D/3D Registration of Acetabular Hip Implants Under Perspective Projection and Fully Differentiable Ellipse Fitting

TL;DR

The paper tackles intra-operative estimation of acetabular cup pose in total hip arthroplasty from AP fluoroscopy by addressing perspective-induced distortions that invalidate simple orthographic assumptions. It introduces a forward model from the 3D cup pose to the 2D image plane under perspective projection and pairs it with a fully differentiable ellipse fitting process, enabling gradient-based optimization over five pose variables $\theta$, $\varphi$, $k$, $l$, and $h$. The authors validate the method across numerical simulations, implant CTs, and cadaver CTs, showing superior angular and translational accuracy compared to orthographic and some 2D/3D registration baselines, with mean registration times around ~1–2 seconds and modest memory requirements. The differentiability of the ellipse fitting facilitates integration with learning-based refinements, supporting practical deployment in the operating room and potential end-to-end optimization pipelines for refined pose estimation under fluoroscopy.

Abstract

This paper presents a novel method for estimating the orientation and the position of acetabular hip implants in total hip arthroplasty using full anterior-posterior hip fluoroscopy images. Our method accounts for distortions induced in the fluoroscope geometry, estimating acetabular component pose by creating a forward model of the perspective projection and implementing differentiable ellipse fitting for the similarity of our estimation from the ground truth. This approach enables precise estimation of the implant's rotation (anteversion, inclination) and the translation under the fluoroscope induced deformation. Experimental results from both numerically simulated and digitally reconstructed radiograph environments demonstrate high accuracy with minimal computational demands, offering enhanced precision and applicability in clinical and surgical settings.

Figures (3)

• Figure 1: Registration pipeline. (a) Segment the ellipse (orange cross-line), extract landmarks $S^P$ (orange point) on the edge of the ellipse, and calculate ellipse $E$ (orange ellipsoidal-line) by fitting an ellipse on $S^P$. (b) Rotate and translate landmarks $\hat{S}$ (red) to $\hat{S}^T$ (light blue), project to obtain $\hat{S}^P$ (purple), and calculate ellipse $\hat{E}$ (purple line) by fitting an ellipse on $\hat{S}^P$. (c) Calculate the difference (red arrow) between $E$ and $\hat{E}$. (d) Update variable $(\hat{\theta},\hat{\varphi},\hat{k},\hat{l},\hat{h})$. Repeat process (b), (c), (d) until convergence.
• Figure 2: Comparison of $\hat{\theta}$ estimation on proposed and orthographic projection Liaw_Hou_Yang_Wu_Fuh_2006b in the simulated environment. From left to right, experiments were conducted when distance from the origin to the object, $(k,l)$, increases from 0, 50, and to 100 mm, while other parameters were fixed. The peak at distance = 0 occurs as $\theta \rightarrow 0$, which causes numerical instability as the ellipse collapses to a line.
• Figure 3: Mean absolute error (MAE) of $\theta$ and $\varphi$ as a function of the distance from the origin to the object, $(k,l)$. Experiments were conducted in the synthetic environment (left) and the DRR environment (right). $\theta$ and $\varphi$ indicate the experiments where each parameters were fixed. Results from intensity and embedding-based registration for implant CT was excluded due to high error.