An Integrated Approach for Simultaneous Calibration and 3-D Coronary Artery Centerline Reconstruction From Two Non-Simultaneous Angiographic Images

The three-dimensional (3D) reconstruction of the coronary artery from angiographic images is crucial for diagnosing and treating coronary artery disease. However, accurate reconstruction is challenging due to the non-simultaneous acquisition of angiographic images and the complex motion patterns of coronary arteries. State-of-the-art methods typically involve a two-stage process: manual selection of corresponding point pairs for spatial geometric calibration, followed by centerline reconstruction. However, overlap and foreshortening in 2D images complicate point selection, often requiring repeated adjustments, and the lack of sufficient point pairs can lead to reconstruction failure. In this paper, we propose a one-stage automatic approach that integrates calibration and 3D centerline reconstruction, eliminating the need for manual calibration. For each angiographic image, we constructed a 3D deformable curve corresponding to the 2D vessel centerline, strictly constrained by the projection lines. Unlike traditional methods that minimize 2D reprojection errors, our approach minimizes the 3D spatial distance between two 3D curves, simultaneously optimizing the spatial transformation and the two deformable 3D curves. The transformation is optimized through iterative curves registration, while the curves are evolved based on a cosine representation method. Both processes occur simultaneously and mutually reinforce each other, resulting in high-precision 3D reconstruction without manual calibration. The proposed approach was validated on 45 phantom and 107 clinical data. The mean space error was $0.085~\pm ~0.085$ mm for phantom data; and the mean reprojection error was $0.060~\pm ~0.027$ mm for clinical data. Results demonstrated that our approach achieves state-of-the-art accuracy while eliminating the need for manual intervention.