Gaussian mixture models based 2D–3D registration of bone shapes for orthopedic surgery planning

In orthopedic surgery, precise kinematics assessment helps the diagnosis and the planning of the intervention. The correct placement of the prosthetic component in the case of knee replacement is necessary to ensure a correct load distribution and to avoid revision of the implant. 3D reconstruction of the knee kinematics under weight-bearing conditions becomes fundamental to understand existing in vivo loads and improve the joint motion tracking. Existing methods rely on the semiautomatic positioning of a shape previously segmented from a CT or MRI on a sequence of fluoroscopic images acquired during knee flexion. We propose a method based on statistical shape models (SSM) automatically superimposed on a sequence of fluoroscopic datasets. Our method is based on Gaussian mixture models, and the core of the algorithm is the maximization of the likelihood of the association between the projected silhouette and the extracted contour from the fluoroscopy image. We evaluated the algorithm using digitally reconstructed radiographies of both healthy and diseased subjects, with a CT-extracted shape and a SSM as the 3D model. In vivo tests were done with fluoroscopically acquired images and subject-specific CT shapes. The results obtained are in line with the literature, but the computational time is substantially reduced.