Global Registration of 3D Cerebral Vessels to Its 2D Projections by a New Branch-and-Bound Algorithm

Endovascular interventions are usually guided by intraoperative 2D images, which cannot fully reflect the 3D structure of vessels and sometimes cause ambiguity. Registering preoperative 3D images to intraoperative 2D images can help eliminate this ambiguity. Most existing methods can only converge to a local optimal solution. Similar to POSE [1], we formulate the problem as 2D-3D point set registration, and develop a fast and accurate global registration method. We propose a novel objective function using consensus set between the 3D points and the projection lines of the 2D points in the 3D space, and introduce a new global optimal rotation search algorithm. The translation search problem is tackled by synchronized grid search in the translation space. Furthermore, we extend the algorithm to register 3D vessels to its two projections, which only increases the runtime slightly but improves the 3D registration accuracy significantly. The proposed method is approximately two times faster than POSE. Experiments on real data show that the mean 3D rotation error is reduced from 5.55 degrees of POSE to 1.62 degrees and the mean translation error is reduced from 8.60 mm of POSE to 1.06 mm by the proposed double-plane method.