We believe the combination of implicit surfaces and the level set method provides a general framework for surface modeling, analysis, reconstruction, deformation and many other applications. We constructed a "weighted" minimal surface model for surface reconstruction from scattered data set using variational formulations and partial differential equations. Our formulation only uses the unsigned distance function to the data set.The reconstructed surface is smoother than piecewise linear and has a regularization that is adaptive to the local sampling density. The formulation handles noisy as well as non-unform data and works in any number of dimensions. We develop efficient and robust numerical algorithms for our formulations. Details can be found in our papers:

• Implicit and Non-parametric Shape Reconstruction from Unorganized Points Using Variational Level Set Method,  (ps file , pdf file)  H.K. Zhao, S. Osher, B. Merriman, M. Kang.   Computer Vision and Image Understanding. Vol. 80, 2000, pp 295-319

 
• Fast Surface Reconstruction and Deformation Using the Level Set Method,  (ps file  , pdf file)   H.K. Zhao, S. Osher, R. Fedkiw.  Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision (VLSM  2001),  July, 2001, Vancouver.

 
• Analysis and Visualization of Large Set of Unorganized Data Points Using the Distance Function,    H.K. Zhao,  submitted  (ps file,  pdf file)

                                                                               Picture Gallery
 

             reconstruction of a sphere from circles                                               hole filling for a torus

                  data                                    reconstruction                                 data                                    reconstruction
 

              reconstruction of a ratbrain from MRI slices of 1506 data points on a 80x77x79 grid

                                                data                                                                    reconstruction
 

       reconstruction of the Happy Buddha from 543,652 data points

reconstruction on a 64x150x64 grid       reconstruction on a 146x350x146 grid
 

                                            reconstruction of the dragon on a 300x212x136 grid

        reconstruction from 100,250 data points                            reconstruction from 437,645 data points

                             reconstruction of a drill bit from 1,961 data points on a 24x250x32 grid
 

 reconstruction of a hand skeleton from 327,323 data points on a 200x141x71 grid
 

reconstruction of a turbine blade from 882,954 data points on a 178x299x139 grid

Acknowledgement:
The data for the Happy Buddha, the dragon and the drill are obtained from The Stanford 3D Scanning Repository.  The data for the hand skeleton and the turbine blade are obtained from Large Geometric
Models Archive.