Title: Guaranteed Simply Connected Mesh Reconstruction from an Unorganized Point Cloud
Primary area: optimization
Keywords: 3D Reconstruction, spectral techniques, topological guarantee, Laplacian, Hodge decomposition

Abstract: We introduce an approach that reconstructs a closed surface mesh from a noisy point cloud, where the topology of surface is guaranteed to be simply connected, i.e., homeomorphic to a topological 2-sphere. This task enjoys a wide range of applications, e.g., 3D organ and vessel reconstruction from CT scans. Central to our approach is a robust module that takes a collection of oriented triangles in a 3D triangulation as input and outputs a simply connected volumetric mesh whose boundary approximates the input triangles. Starting from a 3D Delaunay triangulation of the input point cloud and initial triangle orientations obtained through a spectral approach, our approach alternates between applying the module to obtain a reconstruction and using that reconstruction to reorient the input triangles.  Experimental results on real and synthetic datasets demonstrate the effectiveness of our approach.

TL;DR: An framework that reconstructs a simply connected manifold mesh from a noisy 3D point cloud.