Shape as Line Segments: Accurate and Flexible Implicit Surface Representation

Distance field-based implicit representations like signed/unsigned distance fields have recently gained prominence in geometry modeling and analysis. However, these distance fields are reliant on the closest distance of points to the surface, introducing inaccuracies when interpolating along cube edges during surface extraction. Additionally, their gradients are ill-defined at certain locations, causing distortions in the extracted surfaces. To address this limitation, we propose Shape as Line Segments (SALS), an accurate and efficient implicit geometry representation based on attributed line segments, which can handle arbitrary structures. Unlike previous approaches, SALS leverages a differentiable Line Segment Field to implicitly capture the spatial relationship between line segments and the surface. Each line segment is associated with two key attributes, intersection flag and ratio, from which we propose edge-based dual contouring to extract a surface. We further implement SALS with a neural network, producing a new neural implicit presentation. Additionally, based on SALS, we design a novel learning-based pipeline for reconstructing surfaces from 3D point clouds. We conduct extensive experiments, showcasing the significant advantages of our methods over state-of-the-art methods. The source code is available at https://github.com/rsy6318/SALS.