1. Robust Moving Least-squares Fitting with Sharp Features
Shachar Fleishman, Danieal Cohen-Or and Claudio Silva
SIGGRAPH 2005

2. Difference
Levin’s MLS surface
Robust MLS

3. Currently Research Trend
Statistical method
Using pattern recognition
MPI
Won-Ki Jeong, Ioannis Ivrissimtzis, Hans-Peter Seidel. “Neural Meshes: Statistical Learning based on Normals,” In Proc. Pacific Graphics, 2003.
H.Yamauchi, S.Lee, Y.Lee, Y.Ohtake, A.Belyaev, and H.-P.Seidel, Feature Sensitive Mesh Segmentation with Mean Shift, Shape Modeling International 2005

4. Abstract
Robust moving least-squares technique for reconstructing a piecewise smooth surface from a noisy point cloud
Use robust statistics method
Forward-search paradigm
Define sharp features

5. Contributions
Generate the representation from a noisy data set

6. Background and related work
Surface reconstruction should be insensitive to noise
Generate a piecewise smooth surfaces which adequately represent the sharp features

7. Surface Reconstruction
Pioneering work
Hoppe et al. [1994]
Create a piecewise smooth surface in a multi-phase process
Sharp features
Two polygons whit a crease angle that is higher than a threshold
Ohtake et al. [2003]
Surface representation
Defined by a blend of locally fitted implicit quadrics
Not sensitive to noise

8. Robust statistics methods
Pauly et al. [2004]
Presented a method for measuring the uncertainty of a point set
Xie et al. [2004]
Extended the MPU technique to handle noisy datasets

9. Forward search and iterative refitting

10. Results
Reconstruction
of the fandisk model

11. Results A reconstruction from a raw Deltasphere scan of a pipe
(a) Input data
(b) MLS
(c) Robust MLS
(d) Reconstructed surface (blue), input data (red)

12. Results Reconstruction of missing data
(a) Input data; samples near the edge are missing
(b) MLS
(c) Robust MLS
(d) Points that were projected to the edge are marked in yellow