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An accurate segmentation of vascular systems is fundamental for many medical applications. In this paper, we propose a 3D vessel enhancement and extraction method. It is based on the analysis of Hessian matrix and Gaussian mixture model-expectation-maximization (GMM-EM) algorithm. Firstly, tube-like vessels were detected and enhanced based on the Hessian matrix eigenvalues. And then, the vascular system was segmented, and then a rough system was obtained with GMM-EM. Hessian-based filters were found to be sensitive to noise and sometimes gave discontinued vessels. Hence, we utilized the closing operation to avoid discontinuity and a 3D-filter on the segmented vessels to reduce noise brought by the contrast agent. Finally, a searching method based on spatial connected area is presented to connect the vascular system in 3D. The experimental results illustrated the efficiency of the method for 3D liver vessel segmentation proposed in this paper.