Intraoperative x-ray radiography/fluoroscopy is commonly used to assess the placement of surgical devices in the operating room (e.g. spine pedicle screws), but qualitative interpretation can fail to reliably detect suboptimal delivery and/or breach of adjacent critical structures. We present a 3D-2D image registration method wherein intraoperative radiographs are leveraged in combination with prior knowledge of the patient and surgical components for quantitative assessment of device placement and more rigorous quality assurance (QA) of the surgical product. The algorithm is based on known-component registration (KC-Reg) in which patient-specific preoperative CT and parametric component models are used. The registration performs optimization of gradient similarity, removes the need for offline geometric calibration of the C-arm, and simultaneously solves for multiple component bodies, thereby allowing QA in a single step (e.g. spinal construct with 4-20 screws). Performance was tested in a spine phantom, and first clinical results are reported for QA of transpedicle screws delivered in a patient undergoing thoracolumbar spine surgery. Simultaneous registration of ten pedicle screws (five contralateral pairs) demonstrated mean target registration error (TRE) of 1.1  ±  0.1 mm at the screw tip and 0.7  ±  0.4° in angulation when a prior geometric calibration was used. The calibration-free formulation, with the aid of component collision constraints, achieved TRE of 1.4  ±  0.6 mm. In all cases, a statistically significant improvement (p  <  0.05) was observed for the simultaneous solutions in comparison to previously reported sequential solution of individual components. Initial application in clinical data in spine surgery demonstrated TRE of 2.7  ±  2.6 mm and 1.5  ±  0.8°. The KC-Reg algorithm offers an independent check and quantitative QA of the surgical product using radiographic/fluoroscopic views acquired within standard OR workflow. Such intraoperative assessment could improve quality and safety, provide the opportunity to revise suboptimal constructs in the OR, and reduce the frequency of revision surgery.