Accurate reconstruction of transcatheter aortic valve (TAV) geometries and other stented cardiac devices from computed tomography (CT) images is challenging, mainly associated with blooming artifacts caused by the metallic stents. In addition, bioprosthetic leaflets of TAVs are difficult to segment due to the low signal strengths of the tissues. This paper describes a method that exploits the known device geometry and uses an image registration-based reconstruction method to accurately recover the in vivo stent and leaflet geometries from patient-specific CT images. Error analyses have shown that the geometric error of the stent reconstruction is around 0.1mm, lower than 1/3 of the stent width or most of the CT scan resolutions. Moreover, the method only requires a few human inputs and is robust to input biases. The geometry and the residual stress of the leaflets can be subsequently computed using finite element analysis (FEA) with displacement boundary conditions derived from the registration. Finally, the stress distribution in self-expandable stents can be reasonably estimated by an FEA-based simulation. This method can be used in pre-surgical planning for TAV-in-TAV procedures or for in vivo assessment of surgical outcomes from post-procedural CT scans. It can also be used to reconstruct other medical devices such as coronary stents.