Optimization of transformation for 3D reconstruction of coronary arterial tree

The spatial relationship between two single plane angiograms, which is characterized by transformation in the forms of a rotation matrix and a translation vector, is important for 3D reconstruction of coronary arterial tree. The error of transformation directly reduces the precision of 3D reconstruction. In this study, we introduce the methods of 3D reconstruction, analyze the necessity of optimization of transformation, and define transformation by quaternion. Then bifurcations, vessel vectors and branch angles are employed to optimize the transformation, with Levenberg-Marquardt algorithm. The experimental results on the human angiogram data are presented. The Standard Deviation of reconstruction error reduces from 3.8573 mm to 1.0803 mm in image A and from 4.0663 mm to 1.0742 mm in image B respectively on clinical angiogram data. The results of experiments show that the technique put forward in this paper greatly improves the accuracy of 3D reconstruction.