Shape-based 3D surface reconstructing methods for liver vessels have difficulties to tackle with limited contrast of medical images and the intrinsic complexity of multi-furcation parts. In this paper, we propose an effective and robust technique, called Gap Border Pairing (GBPa), to reconstruct surface of liver vessels with complicated multi-furcations. The proposed method starts from a tree-like skeleton which is extracted from segmented liver vessel volumes and preprocessed as a number of simplified smooth branching lines. Secondly, for each center point of any branching line, an optimized elliptic cross-section ring (contour) is generated by optimizedly fitting its actual cross-section outline based on its tangent vector. Thirdly, a tubular surface mesh is generated for each branching line by weaving all of its adjacent rings. Then for every multi-furcation part, a transitional regular mesh is effectively and regularly reconstructed by using GBP. An initial model is generated after reconstructing all multi-furcation parts. Finally, the model is refined by using just one time subdivision and its topologies can be re-maintained by grouping its facets according to the skeleton, providing high-level editability. Our method can be automatically implemented in parallel if the segmented vessel volume and corresponding skeletons are provided. The experimental results show that GBP model is accurate enough in terms of the boundary deviations between segmented volume and the model. 
An effective and robust method for modeling multi-furcation liver vessel by using Gap Border Pairing