Dynamic chest radiography (2D x-ray video) is a low-dose and cost-effective functional imaging method with high temporal resolution. While the analysis of rib-cage motion has been shown to be effective for evaluating respiratory function, it has been limited to 2D. We aim at 3D rib-motion analysis for high temporal resolution while keeping the radiation dose at a level comparable to conventional examination. To achieve this, we developed a method for automatically recovering 3D rib motion based on 2D-3D registration of x-ray video and single-time-phase computed tomography. We introduce the following two novel components into the conventional intensity-based 2D-3D registration pipeline: (1) a rib-motion model based on a uniaxial joint to constrain the search space and (2) local contrast normalization (LCN) as a pre-process of x-ray video to improve the cost function of the optimization parameters, which is often called the landscape. The effects of each component on the registration results were quantitatively evaluated through experiments using simulated images and real patients' x-ray videos obtained in a clinical setting. The rotation-angle error of the rib and the mean projection contour distance (mPCD) were used as the error metrics. The simulation experiments indicate that the proposed uniaxial joint model improved registration accuracy. By searching the rotation axis along with the rotation angle of the ribs, the rotation-angle error and mPCD significantly decreased from 2.246 ± 1.839° and 1.148 ± 0.743 mm to 1.495 ± 0.993° and 0.742 ± 0.281 mm, compared to simply applying De Troyer's model. The real-image experiments with eight patients demonstrated that LCN improved the cost function space; thus, robustness in optimization resulting in an average mPCD of 1.255 ± 0.615 mm. We demonstrated that an anatomical-knowledge based constraint and an intensity normalization, LCN, significantly improved robustness and accuracy in rib-motion reconstruction using chest x-ray video.