Extraction of brain blood vessels is an important issue for clinical assessment of intracranial vascular diseases. In this paper, the vessel extraction problem is formulated to a connected region classification problem. In processing images, an improved multi-scale filtering method is performed to improve vessel connectivity, and a post-processing step is added to harvest salient vessel candidates (SVC). Then, SVC is decomposed into connected regions and features are calculated and fed into a neural network classifier for training. For extraction, each connected region is individually analyzed using the trained neural network by considering the values of neighboring voxels that belong to its connection. The extraction results demonstrate the validity of the proposed approach.