Poisson surface reconstruction and its applications

Abstract

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, the Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. To reconstruct detailed models in limited memory, we solve this Poisson formulation efficiently using a streaming framework. Specifically, we introduce a multilevel streaming representation, which enables efficient traversal of a sparse octree by concurrently advancing through multiple streams, one per octree level. Remarkably, for our reconstruction application, a sufficiently accurate solution to the global linear system is obtained using a single iteration of cascadic multigrid, which can be evaluated within a single multi-stream pass. Finally, we explore the application of Poisson reconstruction to the setting of multi-view stereo, to reconstruct detailed 3D models of outdoor scenes from collections of Internet images. This is joint work with Michael Kazhdan, Matthew Bolitho, and Randal Burns (Johns Hopkins University), and Michael Goesele, Noah Snavely, Brian Curless, and Steve Seitz (University of Washington).