Biplanar Radiographic 3D Reconstruction of Vertebrae Using Non-stereo Corresponding Points Based on Epipolar Geometry

An approach based on epipolar geometry was proposed for three-dimensional (3D) vertebrae reconstruction from biplanar radiographs. The main contribution was to reconstruct the non-stereo corresponding points (NSCP) under the constraints of both epipolar geometry and vertebral topology. The proposed method first detected the stereo corresponding points (SCP) in biplanar radiographs and estimated the 3D positions of these landmarks based on epipolar geometry. For the NSCP reconstruction, the 3D distances between any two landmarks measured from anatomical primitives were used to define the vertebral topological constraint. The cost of the reconstruction was defined as the sum of the differences between the primitive distances and the reconstructed distances. Since the 3D position of a NSCP was restricted to an epipolar line under the constraint of epipolar geometry, the 3D positions of NSCP were found by searching on the epipolar lines to minimize the reconstruction cost. With the 3D landmarks (including SCP and NSCP) reconstructed as control points, the anatomical primitives were deformed to obtain the personalized vertebral models by using the kriging algorithm. The point-to-surface distances between the biplanar radiographic and CT-scan reconstructions were calculated for two vertebrae (T4 and L2) to validate the proposed method. In the global comparison, the mean distances were less than 2 mm for both vertebrae. In the local comparison, all points were divided in five subgroups. It was shown that the distances were less in the area of pedicles due to more control points reconstructed in there. Compared with the documented reconstruction errors, the results indicate that the proposed method can be used to obtain the 3D geometry of vertebrae from biplanar radiographs.