Reconstructing surfaces from scanned 3D points has been an important research area for several decades. One common approach that has proven efficient and robust to noise is implicit surface reconstruction, i.e. fitting to the points a 3D scalar function (such as an indicator function or signed-distance field) and then extracting an isosurface. Though many techniques fall within this category, existing methods either impose no boundary constraints or impose Dirichlet/Neumann conditions on the surface of a bounding box containing the scanned data. In this work, we demonstrate the benefit of supporting Dirichlet constraints on a general boundary. To this end, we adapt the Screened Poisson Reconstruction algorithm to input a constraint envelope in addition to the oriented point cloud. We impose Dirichlet boundary conditions, forcing the reconstructed implicit function to be zero outside this constraint surface. Using a visual hull and/or depth hull derived from RGB-D scans to define the constraint envelope, we obtain substantially improved surface reconstructions in regions of missing data.

@article{Kazhdan:2020:PSR,
   author = "Misha Kazhdan and Ming Chuang and Szymon Rusinkiewicz and Hugues Hoppe",
   title = "Poisson Surface Reconstruction with Envelope Constraints",
   journal = "Computer Graphics Forum (Proc. Symposium on Geometry Processing)",
   year = "2020",
   month = jul,
   volume = "39",
   number = "5"
}