Not yet reviewed by Pith; the record is open.

Coronary artery extraction is a crucial prerequisite for computer-aided diagnosis of coronary artery disease. Accurately extracting the complete coronary tree remains challenging due to several factors, including presence of thin distal vessels, tortuous topological structures, and insufficient contrast. These issues often result in over-segmentation and under-segmentation in current segmentation methods. To address these challenges, we propose a topology-preserving three-stage framework for fully-connected coronary artery extraction. This framework includes vessel segmentation, centerline reconnection, and missing vessel reconstruction. First, we introduce a new centerline enhanced loss in the segmentation process. Second, for the broken vessel segments, we further propose a regularized walk algorithm to integrate distance, probabilities predicted by a centerline classifier, and directional cosine similarity, for reconnecting the centerlines. Third, we apply implicit neural representation and implicit modeling, to reconstruct the geometric model of the missing vessels. Experimental results show that our proposed framework outperforms existing methods, achieving Dice scores of 88.53\% and 85.07\%, with Hausdorff Distances (HD) of 1.07mm and 1.63mm on ASOCA and PDSCA datasets, respectively. Code will be available at https://github.com/YH-Qiu/CorSegRec.