Author: Jones
Year: 2003
- Mesh Smoothing algorithm applicable to every "triangle soup" with robust statistics
- pb: remove noise while preserving the shape
- previous work: isotropic algorithm (smooth salient features), diffusion equations (significant computationnal time), diffusion on normal field (same as before)
- capture the smoothness of a surface with local first order predictors
- predict the surface of a triangle
$q$ with a tangent plane$\Pi_q$ - estimate the position of a vertex
$p$ based on the predictions$\Pi_q(p)$ - the estimate of a point is then the weighted average of all the predictors of
$q \in S$ $\Pi_q(p)$ on a given surface$S$ $$ p^{\prime}=\frac{1}{k(p)} \sum_{q \in S} \Pi_q(p) a_q f\left(\left|c_q-p\right|\right) g\left(\left|\Pi_q(p)-p\right|\right) $$ with$k(p)$ the normalizing factor: $$ k(p)=\sum_{q \in S} a_q f\left(\left|c_q-p\right|\right) g\left(\left|\Pi_q(p)-p\right|\right) $$ - Then mollification (i.e. smoothing of the normals (with the same method as before ?))