1. CS175 2003 1 CS 175 – Week 4 Triangle Mesh Smoothing Signal Processing, Diffusion, Curvature Flow

2. CS175 2003 2 Overview signal processing diffusion curvature flow

3. CS175 2003 3 Singal Processing Fourier analysis transform signal to frequency space cut of high frequencies (noise) multiplication with box-function transform back to signal space filtering convolution with filter kernal

4. CS175 2003 4 Signal Processing Gaussian filtering repeated averaging not a low-pass filter produces shrinking use negative weight to “unshrink”

5. CS175 2003 5 Diffusion see filtering as diffusion process integration explicit Euler implicit Euler prevent shrinking uniform scaling

6. CS175 2003 6 Discrete Laplace Laplace operator uniform parameterization  (v)= 1/k  i (v i – v) conformal parameterization  (v)= 1/S(v)  i (cot  i +cot  i )(v i – v) gives Laplace-Beltrami gives normal and mean curvature

7. CS175 2003 7 Curvature Flow diffusion with Laplace Beltrami curvature flow high curvature regions move faster no tangential sliding