Learning Delaunay Surface Elements for Mesh Reconstruction

Marie-Julie Rakotosaona1, Paul Guerrero2, Noam Aigerman2, Niloy J. Mitra2,3, Maks Ovsjanikov1

  • 1LIX, Ecole Polytechnique, IP Paris
  • 2Adobe Research
  • 3University College London

We present a method for mesh reconstruction from point clouds. We combine Delaunay triangulations with learned local parameterizations to obtain a higher-quality mesh than the current state-of-the-art. Bad (non-manifold) triangles are shown in red. We compare to PointTriNet [1] and IER Meshing [2].

[1] Nicholas Sharp and Maks Ovsjanikov. Pointtrinet: Learned triangulation of 3d point sets. ECCV, 2020
[2] Minghua Liu, Xiaoshuai Zhang, and Hao Su. Meshing point clouds with predicted intrinsic-extrinsic ratio guidance. ECCV, 2020.


We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties of 2D Delaunay triangulations to construct a mesh from manifold surface elements. Our method first estimates local geodesic neighborhoods around each point. We then perform a 2D projection of these neighborhoods using a learned logarithmic map. A Delaunay triangulation in this 2D domain is guaranteed to produce a manifold patch, which we call a Delaunay surface element. We synchronize the local 2D projections of neighboring elements to maximize the manifoldness of the reconstructed mesh. Our results show that we achieve better overall manifoldness of our reconstructed meshes than current methods to reconstruct meshes with arbitrary topology.


We present Learning Delaunay Surface Elements for Mesh Reconstruction (DSE meshing), for any point in an input point cloud, we select the k-nearest neighbors and extract the subset of points that are in the geodesic neighborhood of the center point, using a learned classification network. A projection network then estimates a log map projection of the points into a 2D embedding, where we can apply Delaunay Triangulation to get a DSE.

We show qualitative comparison of our DSE meshing to state of the art methods below.

We evaluate our method on non uniformly sampled point clouds. Shapes are sampled more densely to the left and more coarsely to the right. We can see that methods struggle to reconstruct the coarsely sampled parts of the point cloud. While our method also has slightly more errors in the coarsely sampled regions, the mesh quality drops by a much smaller amount from densely to coarsely sampled regions.


If you use our work, please cite our paper:

    author    = {Rakotosaona, Marie-Julie and Guerrero, Paul and Aigerman, Noam and Mitra, Niloy J. and Ovsjanikov, Maks},
    title     = {Learning Delaunay Surface Elements for Mesh Reconstruction},
    booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
    month     = {June},
    year      = {2021},
    pages     = {22-31}