Poisson surface reconstruction
Reconstruction that considers all points at once for resilience to data noise.
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
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
and adapted over tetrahedral grids
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.