Variational Surface Reconstruction Using Natural Neighbors

Jianjun Xia, Tao Ju

Washington University in Saint Louis
SIGGRAPH 2025 Best Paper Honorable Mention

Given a point cloud without normals (a) that sparsely samples a thin Helmet (from [Laric 2012], 100K samples), the state-of-the-art normal estimation method [Lin et al. 2024] results in a “holy” helmet (b), while the latest learning-based reconstruction method [Erler et al. 2024] smears the facial features (c). Our method (NN-VIPSS) closely approximates the ground truth (e). Close-up views show a cross-section of the surface.

Abstract

Surface reconstruction from points is a fundamental problem in computer graphics. While numerous methods have been proposed, it remains challenging to reconstruct from sparse and non-uniform point distributions, particularly when normals are absent. We present a robust and scalable method for reconstructing an implicit surface from points without normals. By exploring the locality of natural neighborhoods, we propose local reformulations of a previous global method, known for its ability to surface sparse points but high computational cost, thereby significantly improving its scalability while retaining its robustness. Our method involves a single parameter, requires no discretization, and achieves comparable speed as existing reconstruction methods on large inputs while producing fewer artifacts in under-sampled regions.

Comparing 2D Hermite interpolation using Duchon’s interpolant (a), our NND (b), Sibson’s 𝐶1 coordinates [Sibson 1981] (c), Farin’s 𝐶1 coordinates [Farin 1990] (d), method of [Boissonnat and Cazals 2002] (e), and HRBF with a compactly supported kernel (f). Each function is visualized by colors with contours (top, thick curve is zero contour) and the height surface (bottom).

Comparing the normals and surfaces produced by various methods on sparse samples of 3D shapes (Tori and Bathtub taken from [Huang et al. 2019] and Chair from [Huang et al. 2024]). Points are colored by normal differences with ground truth, and surfaces are colored by per-vertex distances to the original shape (red for distances greater than 0.15). NN-VIPSS uses 𝜆 = 0. WNNC level is 0 for Torus 1 and Chair, and 5 for Torus 2 and Bathtub. All surfaces are produced by NND.

Comparing the normals and surfaces produced by various methods on curve samples (taken from [Huang et al. 2019]). Points are colored by normal differences with VIPSS, and surfaces are colored by distances to the VIPSS surface (red for distances greater than 0.15). NN-VIPSS uses 𝜆 = 0 except Walrus where 𝜆 = 0.0005, and WNNC level is 5. GCNO did not terminate on Torus Wire after running for 30 minutes. All surfaces are produced by NND interpolation except Walrus, where VIPSS and NN-VIPSS use NND and other methods use SPR [Kazhdan and Hoppe 2013].

Comparing the normals and surfaces produced by various methods on points sampled from 3D shapes (Helmet 2 from [Laric 2012] and Mobius from [Lin et al. 2024]). Points are colored by normal differences with ground truth and surfaces are colored by distances to ground truth (red for distances greater than 0.02). NN-VIPSS uses 𝜆 = 0. WNNC level is 0 for Brain and Mobius and 1 for Helmet 2. All surfaces are produced by NND interpolation. Genus is noted (𝑔) for Mobius ground truth and reconstructions.

Paper:

BibTeX

@article{xia2025variational,
        title={Variational Surface Reconstruction Using Natural Neighbors},
        author={Xia, Jianjun and Ju, Tao},
        journal={ACM Transactions on Graphics (TOG)},
        volume={44},
        number={4},
        pages={1--19},
        year={2025},
        publisher={ACM New York, NY, USA}
      }





  
  
    
      
        

          
            This website is licensed under a Creative
            Commons Attribution-ShareAlike 4.0 International License.