A Statistical Approach to Determine Symmetrical Solutions for the Registration of 3D Knee Implant Models to Sagittal Fluoroscopy Images

During the registration of 3D CAD models of metallic knee implant components to single-plane sagittal fluoroscopy images, the 3D pose of each implant component is estimated by maximizing the similarity between its 2D image appearance and the observed fluoroscopy image. Because knee implant components are highly symmetrical with respect to the sagittal plane, two significantly different model poses result in 2D image projections very similar to an observed sagittal fluoroscopy image. Traditional 2D/3D registration algorithms tend to converge to one of these symmetrical poses discarding the other one. This paper presents a method which simultaneously estimates both symmetrical solutions. In order not to limit the proposed method to 3D models with an exact plane of symmetry, a completely data-driven symmetry constraint is used which is imposed to the estimated pose parameters. The algorithm is embedded in a statistical framework which is optimized using a deterministic annealing expectation-maximization approach. The validity of the method is demonstrated by registration of the tibial knee implant component to real and simulated fluoroscopy images.