Developability Approximation for Neural Implicits through Rank Minimization

Developability refers to the process of creating a surface without any tearing or shearing from a two-dimensional plane. It finds practical applications in the fabrication industry. An essential characteristic of a developable 3D surface is its zero Gaussian curvature, which means that either one or both of the principal curvatures are zero. This paper introduces a method for reconstructing an approximate developable surface from a neural implicit surface. The central idea of our method involves incorporating a regularization term that operates on the second-order derivatives of the neural implicits, effectively promoting zero Gaussian curvature. Implicit surfaces offer the advantage of smoother deformation with infinite resolution, overcoming the high polygonal constraints of state-of-the-art methods using discrete representations. We draw inspiration from the properties of surface curvature and employ rank minimization techniques derived from compressed sensing. Experimental results on both developable and non-developable surfaces, including those affected by noise, validate the generalizability of our method.

BuildingNet: Learning to Label 3D Buildings

We introduce BuildingNet: (a) a large-scale dataset of 3D building models whose exteriors are consistently labeled, (b) a graph neural network that labels building meshes by analyzing spatial and structural relations of their geometric primitives. To create our dataset, we used crowdsourcing combined with expert guidance, resulting in 513K annotated mesh primitives, grouped into 292K semantic part components across 2K building models. The dataset covers several building categories, such as houses, churches, skyscrapers, town halls, libraries, and castles. We include a benchmark for evaluating mesh and point cloud labeling. Buildings have more challenging structural complexity compared to objects in existing benchmarks (e.g., ShapeNet, PartNet), thus, we hope that our dataset can nurture the development of algorithms that are able to cope with such large-scale geometric data for both vision and graphics tasks e.g., 3D semantic segmentation, part-based generative models, correspondences, texturing, and analysis of point cloud data acquired from real-world buildings. Finally, we show that our mesh-based graph neural network significantly improves performance over several baselines for labeling 3D meshes.