We propose an approach for extracting cerebral arteries from partial Computed Tomography Angiography (CTA). The challenges of extracting cerebral arteries from CTA come from the fact that arteries are usually surrounded by bones and veins in the lower portion of a CTA volume. There exists strong intensity-value overlap between vessels and surrounding objects. Besides, it is inappropriate to assume the 2D cross sections of arteries are circle or ellipse, especially for abnormal vessels. The navigation of the arteries could change suddenly in the 3D space. In this paper, a method based on level set segmentation is proposed to target this challenging problem. For the lower portion of a CTA volume, we use geodesic active contour method to detect cross section of arteries in the 2D space. The medial axis of the artery is obtained by adaptively tracking along its navigation path. This is done by finding the minimal cross section from cutting the arteries under different angles in the 3D spherical space. This method is highly automated, with minimum user input of providing only the starting point and initial navigation direction of the arteries of interests.