Although tracking methods are efficient and popular for vessel segmentation, they require a seed to initiate an instance of tracking. In this paper, a new method to detect new seeds for tracking of arterial segments from CT angiography (CTA) and to construct a vascular structure is proposed. The proposed algorithm is based on shape analysis of connected components in a volume of interest around a vessel segment which was already extracted by tracking. The eigenvalues of the covariance matrix are used as the shape features for detection. The experimental results on actual clinical data showed that the results totally revealed the arterial tree not hindered by bone or veins. In visual comparison to a method which combines registration and subtraction of both pre-contrast and post-contrast CT volumes, the proposed method produced comparable results to the reference method and were confirmed of its feasibility for clinical use of reducing the cost and burden of patients.