Poisson surface reconstruction

Michael Kazhdan, Matthew Bolitho, Hugues Hoppe.

Symposium on Geometry Processing 2006, 61-70.
(SGP 2021 Test of Time Award.)

Reconstruction that considers all points at once for resilience to data noise.

paper talk cover image award-winning code

Abstract: We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.

Hindsights:

One perceived weakness of this work is that it requires oriented normals at the input points. However, most scanning technologies provide this information, either from line-of-sight knowledge or from adjacent nearby points in a range image. Experiments in [Kazhdan 2005] show that the approach is quite resilient to inaccuracies in the directions of the normals. In our subsequent SGP 2007 paper, we show that the Poisson problem can be solved out-of-core for large models by introducing a multilevel streaming representation of the sparse octree. Our 2013 paper extends the approach for improved geometric fidelity and using a faster hierarchical solver.

The algorithm has been incorporated into MeshLab and VTK, and adapted over tetrahedral grids in CGAL.

In 2011, Michael Kazhdan and Matthew Bolitho received the inaugural SGP Software Award for releasing the library code associated with this work.

And ten years later at SGP 2021, the paper received the inaugural Test of Time Award.