A novel graph-cuts-basedmethod is proposed for reconstructing open surfaces from unordered point sets. Through a boolean operation on the crust around the data set, the open surface problem is translated to a watertight surface problem within a restricted region. Integrating the variationalmodel, Delaunay-based tetrahedralmesh framework and multi-phase technique, the proposed method can reconstruct open surfaces robustly and effectively. Furthermore, a surface reconstruction method with domain decomposition is presented, which is based on the new open surface reconstruction method. This method can handle more general surfaces, such as non-orientable surfaces. The algorithm is designed in a parallel-friendly way and necessary measures are taken to eliminate cracks at the interface between the subdomains. Numerical examples are included to demonstrate the robustness and effectiveness of the proposed method on watertight, open orientable, open non-orientable surfaces and combinations of such
