Traceable Surface Reconstruction

Reconstruction of 3D triangle meshes from point clouds is a topic that has received significant attention for more than two decades. This is partly due to the wide range of applications, and partly due to the ill-posedness of the problem. As a result, there are many plausible solutions to this reconstruction problem.

Depending on the application, specific properties are of interest. In most applications complex three-dimensional objects are scanned. This requires each object to be recorded from several directions since each scan only covers a part of the object as seen from a particular point. A large class of methods proceeds by estimating a volumetric function in 3D, that contains the desired surface as an isocontour.

This is both simple and effective, and the output mesh is easily extracted using isocontour triangulation. However, the output only approximates the original input points, and they are not part of the resulting mesh. Another class of methods solves the arguably harder, combinatorial problem of finding a triangle mesh that connects and hence interpolates a large subset of the input points.

The methods developed in this project use the information about the point cloud being a collection of multiple partial scans. This information has been used in a feature-preserving denoising algorithm, as much of the observed noise in real-world scans is a result of the compositional nature of the point cloud.

As a second contribution, a method that reduces combinatorial reconstruction to a well-posed 2D problem has been proposed. This method also uses information about the scanning process. A third contribution adopts graph convolutional networks for labeling the tetrahedra formed from the input points. It uses only local information and is thereby scalable and parallelizable.