Automated extraction of cerebrovascular is of great importance in understanding the mechanism, diagnosis, and treatment of many cerebrovascular pathologies. However, segmentation of cerebrovascular networks from magnetic resonance angiography (MRA) imagery continues to be challenging because of relatively poor contrast and inhomogeneous backgrounds, and the anatomical variations, complex geometry and topology of the networks themselves. In this paper, we present a novel cerebrovascular segmentation framework that consists of image enhancement and segmentation phases. We aim to remove redundant features, while retaining edge information in shallow features when combining these with deep features. We first employ a Retinex model, which is able to model noise explicitly to aid removal of imaging noise, as well as reducing redundancy within an image and emphasizing the vessel regions, thereby simplifying the subsequent segmentation problem. Subsequently, a reverse edge attention module is employed to discover edge information by paying particular attention to the regions that are not salient in high-level semantic features. The experimental results show that the proposed framework enables the reverse edge attention network to deliver a reliable cerebrovascular segmentation.