VFIR: Vector Fields Implicit Representation for Surface Reconstruction From Point Clouds

Surface reconstruction from point clouds has attracted considerable attention in the computer vision community. Most deep learning-based methods focus on modeling signed distance functions (SDFs) and unsigned distance functions (UDFs). However, SDFs are limited to watertight models, and UDFs are non-differentiable at the surface boundary, hindering the learning of smooth representations. In this paper, we introduce a novel method, VFIR, which leverages neural implicit functions to learn vector fields (VFs) for 3D shape modeling. We enhance the network's fitting capability by displacing points along the predicted vector directions, aiming to reduce the deviation between the generated point cloud and the original input. To accelerate convergence, we introduce a progressive learning strategy that incrementally incorporates denser point clouds and corresponding normals during training. For isosurface extraction, we define truncated vector fields (TVFs) that focus computation around surfaces and present an optimized three-state marching cubes (OT-MC) algorithm tailored to the vector field representation. Extensive experiments demonstrate that VFIR achieves state-of-the-art performance with high accuracy and robustness across diverse 3D models, exhibiting strong generalization capabilities and thus representing a promising solution for surface reconstruction across various applications.