Region segmentation via deep learning and convex optimization

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.