We introduce an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. We represent these edges as a collection of parametric curves (i.e.,~lines, circles, and B-splines). Accordingly, our deep neural network, coined PIE-NET, is trained for parametric inference of edges. The network relies on a region proposal architecture, where a first module proposes an over-complete collection of edge and corner points, and a second module ranks each proposal to decide whether it should be considered. We train and evaluate our method on the ABC dataset, a large dataset of CAD models, and compare our results to those produced by traditional (non-learning) processing pipelines, as well as a recent deep learning based edge detector (EC-NET). Our results significantly improve over the state-of-the-art from both a quantitative and qualitative standpoint.

Both perspectives are useful in practice: parametric inference estimates the tensor of distributional parameters as a whole, while multiway analysis yields its latent factors for interpretation [1]. Both tasks rely fundamentally on tensor decompositions to represent and exploit underlying structure. However, computing tensor decompositions is notoriously difficult. Degeneracy phenomena lead to non-unique or ill-conditioned factorizations [2] and many tensor problems are NP-hard [3], making even approximate computation intractable in general. These issues put into question the reliability of existing tensor-based inference methods. They are particularly pronounced for the canonical polyadic (CP) decomposition [2], which, despite its widespread use, lacks the theoretical guarantees enjoyed by other tensor formats. Computing CP factors, i.e., multiway analysis, with minimal variance across multiple sets of observations would enhance the reliability of multiway analysis and parametric inference, offering practitioners more confidence in their results while reducing the need for extensive data collection. 1

The reviewers felt that this paper provides an interesting and novel approach. The demonstrated approach outperforms the previous state of the art by a large margin. The main concern by reviewers is whether this paper is appropriate for a machine learning conference. All reviewers agree that the submission is a strong application paper that would be a strong submission for a computer vision, graphics, or computational geometry conference. However, the reviewers questioned whether the machine learning novelty in this paper is sufficient for a machine learning conference.

We introduce an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. We represent these edges as a collection of parametric curves (i.e., lines, circles, and B-splines). Accordingly, our deep neural network, coined PIE-NET, is trained for parametric inference of edges. The network relies on a "region proposal" architecture, where a first module proposes an over-complete collection of edge and corner points, and a second module ranks each proposal to decide whether it should be considered. We train and evaluate our method on the ABC dataset, a large dataset of CAD models, and compare our results to those produced by traditional (non-learning) processing pipelines, as well as a recent deep learning based edge detector (EC-NET).