1. A method implemented on a computer having one or more processors and storage for separating vessel branches of a first vessel system from vessel branches of a second vessel system in a three dimension (3D) image, comprising the steps of: segmenting, by vessel segmentation mechanism implemented on the one or more processors, the 3D image to obtain a plurality of vessel branches; extracting, by vessel separation mechanism implemented on the one or more processors, a center line for each of the vessel branches; determining, by the vessel separation mechanism, a first root point associated with the first vessel system and a second root point associated with the second vessel system; tracing, by the vessel separation mechanism, starting from the first root point, along the vessel branches to derive a tracing path; automatically determining, by the vessel separation mechanism, a break point along the tracing path as a voxel of maximum score derived from a weighted sum of a curvature measure of the tracing path and a relative intensity measure of the tracing path, the relative intensity measure being indicative of change of intensity from the first root point to the voxel, where the break point separates the tracing path into a first portion and a second portion; determining, by the vessel separation mechanism, a region of interest in the 3D image based on the break point; assigning, by the vessel separation mechanism, one or more center lines in the region of interest to either the first or the second vessel system; automatically obtaining, by the vessel separation mechanism, a cutting plane in the region of interest by fitting a plane that maximizes a total distance from points on the center lines assigned to the first or second vessel system to the plane; automatically constructing, by vessel labeling mechanism implemented on the one or more processors, a first and a second graph representations for the first and second vessel systems, respectively, based on the center lines assigned to each of the first and second vessel systems and the cutting plane, wherein automatically constructing comprises: extracting the center lines assigned to each of the first and second vessel systems, and constructing parts of the first and second graph representations corresponding to edges and vertexes of the first and second vessel systems, respectively; and labeling, by the vessel labeling mechanism, one or more vessel branches in each of the first and second vessel systems with different labels based on the first and second graph representations.