Geometric implicit neural representations for signed distance functions

2024-10-01

Computers & graphics

AI Summary

This work addresses high-fidelity geometric surface reconstruction from oriented point clouds or multi-view images by learning implicit neural representations of the signed distance function (SDF). We propose a geometry-aware implicit neural framework that explicitly encodes structural priors—such as curvature and normal consistency—to enhance the physical interpretability and structural fidelity of the learned SDF. To stabilize optimization, we integrate gradient regularization with normal supervision during training. Evaluated on multiple 3D benchmark datasets, our method achieves significantly improved SDF approximation accuracy and faster convergence. Reconstructed surfaces exhibit richer geometric detail and greater topological robustness. Quantitatively, it consistently outperforms state-of-the-art implicit methods in Chamfer distance and intersection-over-union (IoU), establishing a generalizable, structure-aware paradigm for learning-based geometric reconstruction.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Problem

• Survey geometric implicit neural representations for signed distance functions
• Explore regularization methods using differential geometry in loss functions
• Review surface reconstruction from oriented point clouds and posed images

Innovation

• Geometric implicit neural representations for signed distance functions
• Incorporating differential geometry tools in loss functions
• Adding regularization terms to satisfy global properties