The Taub Faculty of Computer Science Events and Talks

In this talk we consider the problem of manifold reconstruction from oriented point clouds for embedded manifolds of co-dimension larger than one. Using the framework of Poisson Surface Reconstruction, and formulating the problem in the language of alternating products, we show that the earlier approach for reconstructing hyper-surfaces extends to general manifolds, at the cost of replacing a quadratic energy with a multi-quadratic energy. We provide an efficient iterative hierarchical solver that empirically converges to a good reconstruction. We show examples reconstructing curves in 3D and surfaces in 4D. And we validate that the approach remains stable in the presence of sampling and noise.