  Deformable registration of two-dimensional/three-dimensional (2D/3D) images
of abdominal organs is a complicated task because the abdominal organs deform
significantly and their contours are not detected in two-dimensional X-ray
images. We propose a supervised deep learning framework that achieves 2D/3D
deformable image registration between 3D volumes and single-viewpoint 2D
projected images. The proposed method learns the translation from the target 2D
projection images and the initial 3D volume to 3D displacement fields. In
experiments, we registered 3D-computed tomography (CT) volumes to digitally
reconstructed radiographs generated from abdominal 4D-CT volumes. For
validation, we used 4D-CT volumes of 35 cases and confirmed that the 3D-CT
volumes reflecting the nonlinear and local respiratory organ displacement were
reconstructed. The proposed method demonstrate the compatible performance to
the conventional methods with a dice similarity coefficient of 91.6 \% for the
liver region and 85.9 \% for the stomach region, while estimating a
significantly more accurate CT values.
