Sepehr Gholami
Faculty of Mathematics, Statistics and Computer Science, Department of Computer, University of Tehran, Tehran
Surface reconstruction from point clouds is a fundamental problem in computational geometry and 3D modeling. Classical methods based on k-NN graphs and Poisson reconstruction often suffer from reduced accuracy and topological instability in the presence of noise and regions with strong geometric variations. In this paper, we propose a novel method for constructing a geometrically consistent neighborhood graph to achieve robust surface reconstruction from point clouds. Unlike standard distance-based graphs, the proposed approach models point connectivity using a combination of Euclidean distance and normal vector differences, and applies a geometric consistency criterion to remove edges that are inconsistent with the local manifold structure. We introduce a novel geometric consistency criterion that enforces local manifold preservation during graph construction. Furthermore, an adaptive weighting scheme based on local geometric features is introduced to simultaneously preserve high-curvature regions while reducing the effect of noise in smooth areas. Surface reconstruction is then formulated as an optimization process built upon the constructed graph. Experimental evaluations on the Stanford Bunny dataset and synthetic noisy point clouds demonstrate that the proposed method outperforms k-NN Graph and Poisson Reconstruction in preserving geometric details and reducing reconstruction error, achieving a Chamfer Distance of 0.014 and a Hausdorff Distance of 0.062, representing up to 30% improvement over baseline methods.