Poisson Surface Reconstruction

Definition

Given an oriented point cloud (points + normals), the normals are samples of the gradient of the indicator function $\chi$ (1 inside, 0 outside). PSR finds the function whose gradient best matches them, then extracts the surface.

Formula

$$V(x)=\sum _{i}F(x,x_i)n_{i}f=\arg \underset{g}{\min }{\int }_B\Vert V(x)-\nabla g(x){\Vert }_2^{2}dx⟺\Delta f=\nabla \cdot V$$

Solved with finite elements on an octree and a multigrid solver. Screened PSR adds $+\alpha {\sum }_{i}g(p_i{)}^2$.

• Output: watertight mesh, robust to noise, global.
• Needs normals. Tends to over-smooth; screened PSR fits the samples better.
• Only gives the likeliest surface. Neural Stochastic Screened PSR models the distribution over all surfaces.

Appears in

• Lecture 5, Poisson Surface Reconstruction
• Lecture 5, Screened PSR
• Lecture 4, Multi-view stereopsis: oriented patches → mesh
• Lecture 1, course overview

Related concepts

• Point Cloud
• Occupancy Field
• Marching Cubes
• Mesh