Enhancement, followed by segmentation, quantification and modelling of blood vessels in retinal images plays an essential role in computer-aided retinopathy diagnosis. In this paper, we introduce the bowler-hat transform method a new approach based on mathematical morphology for vessel enhancement. The proposed method combines different structuring elements to detect innate features of vessel-like structures. We evaluate the proposed method qualitatively and quantitatively and compare it with the state-of-the-art methods using both synthetic and real datasets. Our results establish that the proposed method achieves high-quality vessel-like structure enhancement in both synthetic examples and clinically relevant retinal images. The bowler-hat transform is shown to be able to detect fine vessels while still remaining robust at junctions.