Classical surgery is being overtaken by minimally invasive and transcatheter procedures. As there is no direct view or access to the affected anatomy, advanced imaging techniques such as 3D C-arm computed tomography (CT) and C-arm fluoroscopy are routinely used in clinical practice for intraoperative guidance. However, due to constraints regarding acquisition time and device configuration, intraoperative modalities have limited soft tissue image quality and reliable assessment of the cardiac anatomy typically requires contrast agent, which is harmful to the patient and requires complex acquisition protocols. We propose a probabilistic sparse matching approach to fuse high-quality preoperative CT images and nongated, noncontrast intraoperative C-arm CT images by utilizing robust machine learning and numerical optimization techniques. Thus, high-quality patient-specific models can be extracted from the preoperative CT and mapped to the intraoperative imaging environment to guide minimally invasive procedures. Extensive quantitative experiments on 95 clinical datasets demonstrate that our model-based fusion approach has an average execution time of 1.56 s, while the accuracy of 5.48 mm between the anchor anatomy in both images lies within expert user confidence intervals. In direct comparison with image-to-image registration based on an open-source state-of-the-art medical imaging library and a recently proposed quasi-global, knowledge-driven multi-modal fusion approach for thoracic-abdominal images, our model-based method exhibits superior performance in terms of registration accuracy and robustness with respect to both target anatomy and anchor anatomy alignment errors.