BIDGCN: boundary-informed dynamic graph convolutional network for adaptive spline fitting of scattered data

Surface reconstruction from scattered point clouds is the process of generating surfaces from unstructured data configurations retrieved using an acquisition device such as a laser scanner. Smooth surfaces are possible with the use of spline representations, an established mathematical tool in computer-aided design and related application areas. One key step in the surface reconstruction process is the parameterization of the points, that is, the construction of a proper mapping of the 3D point cloud to a planar domain that preserves surface boundary and interior points. Despite achieving a remarkable progress, existing heuristics for generating a suitable parameterization face challenges related to the accuracy, the robustness with respect to noise, and the computational efficiency of the results. In this work, we propose a boundary-informed dynamic graph convolutional network (BIDGCN) characterized by a novel boundary-informed input layer, with special focus on applications related to adaptive spline approximation of scattered data. The newly introduced layer propagates given boundary information to the interior of the point cloud, in order to let the input data be suitably processed by successive graph convolutional network layers. We apply our BIDGCN model to the problem of parameterizing three-dimensional unstructured data sets over a planar domain. A selection of numerical examples shows the effectiveness of the proposed approach for adaptive spline fitting with (truncated) hierarchical B-spline constructions. In our experiments, improved accuracy is obtained, e.g., from 60% up to 80% for noisy data, while speedups ranging from 4 up to 180 times are observed with respect to classical algorithms. Moreover, our method automatically predicts the local neighborhood graph, leading to much more robust results without the need for delicate free parameter selection.