Atlas-Based Reconstruction of 3D Volumes of a Lower Extremity from 2D Calibrated X-ray Images

In this paper, reconstruction of 3D volumes of a complete lower extremity (including both femur and tibia) from a limited number of calibrated X-ray images is addressed. We present a novel atlas-based method combining 2D-2D image registration-based 3D landmark reconstruction with a B-spline interpolation. In our method, an atlas consisting of intensity volumes and a set of predefined, sparse 3D landmarks, which are derived from the outer surface as well as the intramedullary canal surface of the associated anatomical structures, are used together with the input X-ray images to reconstruct 3D volumes of the complete lower extremity. Robust 2D-2D image registrations are first used to match digitally reconstructed radiographs, which are generated by simulating X-ray projections of an intensity volumes, with the input X-ray images. The obtained 2D-2D non-rigid transformations are used to update the locations of the 2D projections of the 3D landmarks in the associated image views. Combining updated positions for all sparse landmarks and given a grid of B-spline control points, we can estimate displacement vectors on all control points, and further to estimate the spline coefficients to yield a smooth volumetric deformation field. To this end, we develop a method combining the robustness of 2D-3D landmark reconstruction with the global smoothness properties inherent to B-spline parametrization.