Curvature-Guided Graph and Energy Optimization for Robust Surface Reconstruction of Point Clouds

Sepehr Gholami
Faculty of Mathematics, Statistics and Computer Science, Department of Computer, University of Tehran, Tehran

This paper presents a curvature-guided graph and energy optimization framework for robust surface reconstruction from unstructured point clouds. The proposed method addresses challenges caused by noise and non-uniform sampling by integrating curvature-aware geometric modeling with energy-based surface optimization. Our main contributions are threefold. First, we introduce a curvature-guided adaptive graph construction strategy that encodes local geometric structures more faithfully by combining spatial proximity with curvature-sensitive weighting. Second, we propose a novel surface consistency energy that jointly enforces geometric fidelity and smoothness while explicitly preserving sharp features through curvature-aware regularization. Third, we design an efficient iterative optimization scheme that improves reconstruction quality while maintaining computational efficiency. In the first stage, an adaptive k-nearest neighbor graph is constructed using the proposed curvature-aware weighting, followed by an initial mesh generation via a triangulation-based reconstruction scheme. In the second stage, the proposed energy function is minimized iteratively to refine surface consistency and feature preservation. Extensive experiments on synthetic datasets and real-world LiDAR scans demonstrate that the proposed method outperforms classical approaches such as Poisson Surface Reconstruction and Ball Pivoting Algorithm, as well as recent learning-based methods, in terms of Chamfer Distance, normal consistency, and feature preservation, while maintaining competitive computational cost.