In this paper, we propose three ideas to improve a kinematic estimation algorithm for total knee arthroplasty. The first is a two-step estimation algorithm that improves estimation accuracy by excluding certain assumptions needed for the pattern matching algorithm reported by Banks and Hodge. The second is incorporating a 3D geometric articulation model into the algorithm to improve estimation accuracy substantially for the depth translation, and to introduce contact points' trajectories between the articular surfaces. The third is an algorithm to process estimation even when the silhouettes of two components overlap. To assess our algorithm's potential for clinical application, we carried out two experiments. First, we used a robot to position the prosthesis. Estimation accuracy was checked by comparing input data to the robot with the estimates from X-ray photographs. Incorporating our articulation model remarkably reduced the error in the depth translation. Next, we performed a clinical assessment by applying the algorithm and articulation model to fluoroscopy images of a patient who had recently had TKA.

We have developed a technique for estimating 3D motion of knee prosthesis from its 2D perspective projections. As Fourier descriptors were used for compact representation of library templates and contours extracted from the prosthetic X-ray images, the entire silhouette contour of each prosthetic component was required. This caused such a problem as our algorithm did not function when the silhouettes of tibio and femoral components overlapped with each other. Here we planned a novel method to overcome it; which was processed in two steps. First, the missing part of silhouette contour due to overlap was interpolated using a free-formed curvature such as Bezier. Then the first step position/orientation estimation was performed. In the next step, a clipping window was set in the projective coordinate so as to separate the overlapped silhouette drawn using the first step estimates. After that the localized library whose templates were clipped in shape was prepared and the second step estimation was performed. Computer model simulation demonstrated sufficient accuracies of position/orientation estimation even for overlapped silhouettes; equivalent to those without overlap.

We will propose two innovative techniques for estimating 3D motion of the knee prosthesis from its 2D perspective projections such as X-ray images. One of our proposing techniques is a two-step estimation algorithm and the other is a way to solve overlapping problem. In our two-step estimation algorithm, the first step estimation was done, in the same way as Banks and Hodge's on the assumption of orthogonal projection. Then, the second step estimation was succeeded based upon the perspective projection to accomplish more accurate estimation. The other is a novel method to solve such a problem as our algorithm did not function when the silhouettes of tibio and femoral components overlapped with each other. Here the estimation was processed in two steps in associate with the above-mentioned two-step estimation. First, the missing part of silhouette contour due to overlap was interpolated using free-formed curvatures. In the next step, a clipping window was set in the projective coordinate so as to separate the overlapped silhouette. Simulation results demonstrated that our two-step estimation algorithm improved accuracies much, and also sufficient accuracies could be assured even for the overlapped silhouettes; equivalent to those without overlap.