2-D–3-D Frequency Registration Using a Low-Dose Radiographic System for Knee Motion Estimation

In this paper, a new method is presented to study the feasibility of the pose and the position estimation of bone structures using a low-dose radiographic system, the entrepreneurial operating system (designed by EOS-Imaging Company). This method is based on a 2-D-3-D registration of EOS bi-planar X-ray images with an EOS 3-D reconstruction. This technique is relevant to such an application thanks to the EOS ability to simultaneously make acquisitions of frontal and sagittal radiographs, and also to produce a 3-D surface reconstruction with its attached software. In this paper, the pose and position of a bone in radiographs is estimated through the link between 3-D and 2-D data. This relationship is established in the frequency domain using the Fourier central slice theorem. To estimate the pose and position of the bone, we define a distance between the 3-D data and the radiographs, and use an iterative optimization approach to converge toward the best estimation. In this paper, we give the mathematical details of the method. We also show the experimental protocol and the results, which validate our approach.