Graph-based Point Cloud Surface Reconstruction using B-Splines

2025-09-19

AI Summary

To address the limitations of existing point cloud surface reconstruction methods—namely, reliance on normal vectors, fixed control point counts, and insufficient robustness to noise—this paper proposes a dictionary-guided graph convolutional B-spline surface reconstruction framework. Our method eliminates the need for input point normals and jointly learns both the number and 3D positions of B-spline control points in an end-to-end manner, leveraging a learnable control point dictionary integrated with a graph neural network. This enables adaptive geometric complexity modeling. The resulting architecture inherently supports topological flexibility while preserving geometric continuity. Quantitative evaluations on multiple benchmark datasets demonstrate significant improvements over state-of-the-art approaches in standard metrics—including Chamfer distance and F-Score—as well as superior qualitative visual fidelity. Notably, our method exhibits enhanced robustness under high-noise conditions, achieving more accurate and stable surface reconstructions.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: 3D Computer Vision
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Generating continuous surfaces from discrete point cloud data is a fundamental task in several 3D vision applications. Real-world point clouds are inherently noisy due to various technical and environmental factors. Existing data-driven surface reconstruction algorithms rely heavily on ground truth normals or compute approximate normals as an intermediate step. This dependency makes them extremely unreliable for noisy point cloud datasets, even if the availability of ground truth training data is ensured, which is not always the case. B-spline reconstruction techniques provide compact surface representations of point clouds and are especially known for their smoothening properties. However, the complexity of the surfaces approximated using B-splines is directly influenced by the number and location of the spline control points. Existing spline-based modeling methods predict the locations of a fixed number of control points for a given point cloud, which makes it very difficult to match the complexity of its underlying surface. In this work, we develop a Dictionary-Guided Graph Convolutional Network-based surface reconstruction strategy where we simultaneously predict both the location and the number of control points for noisy point cloud data to generate smooth surfaces without the use of any point normals. We compare our reconstruction method with several well-known as well as recent baselines by employing widely-used evaluation metrics, and demonstrate that our method outperforms all of them both qualitatively and quantitatively.

Problem

• Reconstructing continuous surfaces from noisy point clouds
• Eliminating dependency on ground truth normals
• Adaptively predicting B-spline control points count and location

Innovation

• Dictionary-Guided Graph Convolutional Network strategy
• Predicts both location and number of control points
• Generates smooth surfaces without using point normals