1. CS175 2003 1 CS 175 – Week 2 Processing Point Clouds Local Surface Properties, Moving Least Squares

2. CS175 2003 2 Overview local properties from point cloud moving least squares

3. CS175 2003 3 Local Surface Properties first order estimate eigenvectors u 0, u 1, u 2 and - values 0 · 1 · 2 of covariance matrix u 0 : normal u 1,u 2 : least-square plane u 2 : least-square line surface variation: 0 /( 0 + 1 + 2 )

4. CS175 2003 4 Local Surface Properties higher order estimates local coordinate frame u 0, u 1, u 2 project into (u 1,u 2 )-plane compute best-fitting polynomial use derivatives of polynomial

5. CS175 2003 5 Moving Least Squares create smooth approximation project 3D points near the surface create local reference frame vary frame smoothly everywhere project onto local polynomial collect all projections

6. CS175 2003 6 Moving Least Squares properties projection operator 2-manifold surface as smooth as weight function approximation order = degree of local polynomial + 1