Screened poisson surface reconstruction

TLDR

Poisson surface reconstruction generates watertight surfaces from oriented point sets, and unlike other techniques, its screening term is defined over a sparse set of points rather than the full domain. The study extends Poisson surface reconstruction to explicitly incorporate points as interpolation constraints. This extension generalizes the framework to a screened Poisson equation, retains the same finite‑element discretization, and allows the modified linear system to be solved with a multigrid approach. The sparse constraints can be integrated efficiently, and algorithmic improvements reduce solver time complexity to linear in the number of points, enabling faster, higher‑quality reconstructions.

Abstract

Poisson surface reconstruction creates watertight surfaces from oriented point sets. In this work we extend the technique to explicitly incorporate the points as interpolation constraints. The extension can be interpreted as a generalization of the underlying mathematical framework to a screened Poisson equation. In contrast to other image and geometry processing techniques, the screening term is defined over a sparse set of points rather than over the full domain. We show that these sparse constraints can nonetheless be integrated efficiently. Because the modified linear system retains the same finite-element discretization, the sparsity structure is unchanged, and the system can still be solved using a multigrid approach. Moreover we present several algorithmic improvements that together reduce the time complexity of the solver to linear in the number of points, thereby enabling faster, higher-quality surface reconstructions.