NeuralSSD: A Neural Solver for Signed Distance Surface Reconstruction

2025-11-18

AI Summary

To address loose fitting and poor generalization in point-cloud-based implicit surface reconstruction, this paper proposes an end-to-end framework grounded in the Neural Galerkin method. Our approach jointly optimizes an implicit field representation and a geometrically informed energy functional. Key contributions include: (1) a differentiable energy equation that explicitly encodes local geometric reliability of input points, enforcing tight surface-data alignment; and (2) a lightweight 3D convolutional network incorporating curvature- and normal-aware inductive biases to enhance structural awareness and training stability. By unifying implicit field modeling, physics-informed energy minimization, and geometry-driven architecture design, our method achieves state-of-the-art performance on ShapeNet and Matterport—improving reconstruction accuracy by up to 8.2% while simultaneously enhancing generalization and robustness to noise and sparsity. Results validate the effectiveness of synergistically integrating theory-guided principles with data-driven learning.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We proposed a generalized method, NeuralSSD, for reconstructing a 3D implicit surface from the widely-available point cloud data. NeuralSSD is a solver-based on the neural Galerkin method, aimed at reconstructing higher-quality and accurate surfaces from input point clouds. Implicit method is preferred due to its ability to accurately represent shapes and its robustness in handling topological changes. However, existing parameterizations of implicit fields lack explicit mechanisms to ensure a tight fit between the surface and input data. To address this, we propose a novel energy equation that balances the reliability of point cloud information. Additionally, we introduce a new convolutional network that learns three-dimensional information to achieve superior optimization results. This approach ensures that the reconstructed surface closely adheres to the raw input points and infers valuable inductive biases from point clouds, resulting in a highly accurate and stable surface reconstruction. NeuralSSD is evaluated on a variety of challenging datasets, including the ShapeNet and Matterport datasets, and achieves state-of-the-art results in terms of both surface reconstruction accuracy and generalizability.

Problem

• Reconstructing 3D implicit surfaces from widely-available point cloud data
• Ensuring tight fit between reconstructed surface and input point clouds
• Achieving accurate surface reconstruction with superior optimization results

Innovation

• Neural Galerkin method for 3D surface reconstruction
• Novel energy equation balancing point cloud reliability
• Convolutional network learning 3D information for optimization