  We consider constructing a surface from a given set of point cloud data. We
explore two fast algorithms to minimize the weighted minimum surface energy in
[Zhao, Osher, Merriman and Kang, Comp.Vision and Image Under., 80(3):295-319,
2000]. An approach using Semi-Implicit Method (SIM) improves the computational
efficiency through relaxation on the time-step constraint. An approach based on
Augmented Lagrangian Method (ALM) reduces the run-time via an Alternating
Direction Method of Multipliers-type algorithm, where each sub-problem is
solved efficiently. We analyze the effects of the parameters on the level-set
evolution and explore the connection between these two approaches. We present
numerical examples to validate our algorithms in terms of their accuracy and
efficiency.
