VoroMesh: Learning Watertight Surface Meshes with Voronoi Diagrams
Nissim Maruani Roman Klokov Maks Ovsjanikov Pierre Alliez Mathieu Desbrun
In stark contrast to the case of images, finding a concise, learnable
discrete representation of 3D surfaces remains a challenge. In particular,
while polygon meshes are arguably the most common surface representation used
in geometry processing, their irregular and combinatorial structure often make
them unsuitable for learning-based applications. In this work, we present
VoroMesh, a novel and differentiable Voronoi-based representation of watertight
3D shape surfaces. From a set of 3D points (called generators) and their
associated occupancy, we define our boundary representation through the Voronoi
diagram of the generators as the subset of Voronoi faces whose two associated
(equidistant) generators are of opposite occupancy: the resulting polygon mesh
forms a watertight approximation of the target shape's boundary. To learn the
position of the generators, we propose a novel loss function, dubbed VoroLoss,
that minimizes the distance from ground truth surface samples to the closest
faces of the Voronoi diagram which does not require an explicit construction of
the entire Voronoi diagram. A direct optimization of the Voroloss to obtain
generators on the Thingi32 dataset demonstrates the geometric efficiency of our
representation compared to axiomatic meshing algorithms and recent
learning-based mesh representations. We further use VoroMesh in a
learning-based mesh prediction task from input SDF grids on the ABC dataset,
and show comparable performance to state-of-the-art methods while guaranteeing
closed output surfaces free of self-intersections.