Abstract
Purpose
To achieve 3D kinematic analysis of total knee arthroplasty (TKA), 2D/3D registration techniques, which use X-ray fluoroscopic images and computer-aided design model of the knee implants, have been applied to clinical cases. In previous feature-based registration methods, only edge contours originated from knee implants are assumed to be extracted from X-ray images before 2D/3D registration. Due to the influence of bone and bone-cement close to knee implants, however, edge detection methods extract unwanted spurious edges and noises in clinical images. Thus, time-consuming and labor-intensive manual operations are often necessary to remove the unwanted edges. It has been a serious problem for clinical applications, and there is a strong demand for development of improved method. The purpose of this study was to develop a pose estimation method to perform accurate 2D/3D registration even if spurious edges and noises exist in knee images.
Methods
Our 2D/3D registration technique is based on a feature-based algorithm, and contour points from X-ray images are extracted by Gaussian Laplacian filter and zero crossing methods.
The basic principle of the algorithm is that the 3D pose of a model can be determined by projecting rays from contour points in an image back to the X-ray focus and noting that all of these rays are tangential to the model surface. Therefore, 3D poses are estimated by minimizing the sum of Euclidean distances between all projected rays and the model surface. Additionally, we introduce robust statistics into the 3D pose estimation method to perform accurate 2D/3D registration even if spurious edges and noises exist in knee images. The robust estimation method employs weight functions to reduce the influence of spurious edges and noises. The weight functions are defined for each contour point, and optimization is performed after the weight functions are multiplied to a cost function.
Experimental results
The accuracy and stability validation were performed using in vivo images. The effects of robust estimation were evaluated by comparison with non-robust estimation. One image contained spurious edges and noises, and the other image didn't (they were erased manually). We applied robust and non-robust methods to each image (300 frames). As correct poses, we used the poses which were got by applying previous method to the contour images which spurious edges and noises didn't exist. The root mean square errors (RMSE) and success rate were calculated, and the success rate was defined as the rate of satisfying clinical required accuracy (error is less than 1mm, 1 degree).
As results of the experiments, when non-robust method was applied to contour images in which spurious edges and noises exist, RMSE was too large and success rate was 0 %. However, when robust method was applied to the same images, RMSE was less than 1 mm, 1 degree, and the success rate was about 60 percent. Fig. 1 shows typical result of the experiment.
Conclusions
We have developed a robust 3D kinematic estimation method of TKA from X-ray images, and the method was found to be helpful for analyzing TKA kinematics without labor-intensive operations.
