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.