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

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Presentation transcript:

CS CS 175 – Week 2 Processing Point Clouds Local Surface Properties, Moving Least Squares

CS Overview local properties from point cloud moving least squares

CS 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 /( )

CS 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

CS 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

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