  In this paper, we propose a method to segment regions in three-dimensional
point clouds. We assume that (i) the shape and the number of regions in the
point cloud are not known and (ii) the point cloud may be noisy. The method
consists of two steps. In the first step we use a deep neural network to
predict the probability that a pair of small patches from the point cloud
belongs to the same region. In the second step, we use a convex-optimization
based method to improve the predictions of the network by enforcing consistency
constraints. We evaluate the accuracy of our method on a custom dataset of
convex polyhedra, where the regions correspond to the faces of the polyhedra.
The method can be seen as a robust and flexible alternative to the famous
region growing segmentation algorithm. All reported results are reproducible
and come with easy to use code that could serve as a baseline for future
research.
