NumGrad-Pull: Numerical Gradient Guided Tri-plane Representation for Surface Reconstruction from Point Clouds

TL;DR

NumGrad-Pull tackles surface reconstruction from unoriented point clouds by learning a neural signed distance function (SDF) using a hybrid explicit–implicit tri-plane representation that enables fast queries and high fidelity. It introduces numerical gradients to stabilize training of grid-based tri-planes, and a progressive tri-plane expansion to accelerate convergence. A dual data-sampling strategy provides both dense near-surface supervision and global regularization, reducing artifacts. Across ShapeNet, ABC, FAMOUS, and real scans, NumGrad-Pull achieves state-of-the-art or competitive accuracy with improved robustness and efficiency.

Abstract

Reconstructing continuous surfaces from unoriented and unordered 3D points is a fundamental challenge in computer vision and graphics. Recent advancements address this problem by training neural signed distance functions to pull 3D location queries to their closest points on a surface, following the predicted signed distances and the analytical gradients computed by the network. In this paper, we introduce NumGrad-Pull, leveraging the representation capability of tri-plane structures to accelerate the learning of signed distance functions and enhance the fidelity of local details in surface reconstruction. To further improve the training stability of grid-based tri-planes, we propose to exploit numerical gradients, replacing conventional analytical computations. Additionally, we present a progressive plane expansion strategy to facilitate faster signed distance function convergence and design a data sampling strategy to mitigate reconstruction artifacts. Our extensive experiments across a variety of benchmarks demonstrate the effectiveness and robustness of our approach. Code is available at https://github.com/CuiRuikai/NumGrad-Pull

Figures (6)

• Figure 1: We present NumGrad-Pull, a tri-plane-based framework that enables efficient and robust surface reconstruction from unoriented point sets.
• Figure 2: Illustration of our method. (a) The NumGrad-Pull framework parameterizes a neural signed distance function using a hybrid explicit-implicit representation. We employ a tri-plane structure to store explicit spatial information and a shallow MLP to decode features extracted from the tri-plane implicitly, enabling efficient and robust surface reconstruction from unoriented point sets. (b) For a given query point, our method extracts features from each of the three orthogonal planes via bilinear interpolation. (c) To address locality issues and stabilize the training process, we introduce a numerical gradient computation strategy, which involves adjacent grid entities in back-propagation, ensuring smoother feature propagation across the tri-plane. (d) Using the signed distance and numerical gradients obtained from the tri-plane-based SDF, our method trains the network by pulling the query point toward its nearest neighbor on the surface.
• Figure 3: Visual comparisons of surface reconstruction quality on the synthetic datasets (ABC abc_koch, FAMOUS point2surf_erler, ShapeNet shapenet_chang) and the real-world scan dataset (SBR williams2019deep).
• Figure 4: Visual comparisons of surface reconstruction quality on the 3D Scene dataset 10.1145/2461912.2461919.
• Figure 5: Visual results of surface reconstruction using different tri-plane resolutions.