Deposited in DRO : 01 August 2018 Version of attached le : Accepted Version Peer-review status of attached

Enhancement and detection of 3D vessel-like structures has long been an open problem as most existing image processing methods fail in many aspects, including a lack of uniform enhancement between vessels of different radii and a lack of enhancement at the junctions. Here, we propose a method based on mathematical morphology to enhance 3D vessel-like structures in biomedical images. The proposed method, 3D bowler-hat transform, combines sphere and line structuring elements to enhance vessel-like structures. The proposed method is validated on synthetic and real data, and compared with state-of-the-art methods. Our results show that the proposed method achieves a highquality vessel-like structures enhancement in both synthetic and real biomedical images, and is able to cope with variations in vessels thickness throughout vascular networks while remaining robust at junctions.