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<p>Surface reconstruction is a fundamental and critical task in computer graphics, computer vision, and geometric modeling. Recent learning-based reconstruction methods have made significant progress, but reconstructing high-quality surfaces from unoriented point clouds remains very challenging. This paper tackles this issue by directly learning a neural implicit representation from raw point clouds, leveraging the power of multilevel tensor product B-spline hash encoding and viscosity regularization. Our approach consists of two key components: (1) A hybrid representation model utilizes multilevel tensor product B-spline functions to parameterize the bounding box of point clouds for positional encoding and MLPs for representing implicit functions. Using cubic B-spline functions, our positional encoding can achieve <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="371_2025_3969_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> continuity which is crucial to the quality of reconstruction. To reduce memory usage and speed up convergence, we employ a hash table to store the coefficients of B-spline basis functions; (2) A new loss function integrates data, viscosity, Hessian, and minimal surface terms. Our innovation lies the introduction of the viscosity term, inspired by the vanishing viscosity method, to alleviate the instability in the optimization process and yield a smooth signed distance function solution. To prevent undesired shape variations and ghost geometries, the loss function also incorporates the Hessian term and the minimal surface term. Extensive experimental results demonstrate that our method effectively captures intricate geometric and topological details and outperforms existing reconstruction methods in both quality and accuracy across a diverse range of 3D datasets.</p>

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High-quality neural surface reconstruction from unoriented point clouds via multilevel tensor product B-spline hash encoding and viscosity regularization

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Yixiao Feng,
  • Weihua Tong,
  • Zhangjin Huang

摘要

Surface reconstruction is a fundamental and critical task in computer graphics, computer vision, and geometric modeling. Recent learning-based reconstruction methods have made significant progress, but reconstructing high-quality surfaces from unoriented point clouds remains very challenging. This paper tackles this issue by directly learning a neural implicit representation from raw point clouds, leveraging the power of multilevel tensor product B-spline hash encoding and viscosity regularization. Our approach consists of two key components: (1) A hybrid representation model utilizes multilevel tensor product B-spline functions to parameterize the bounding box of point clouds for positional encoding and MLPs for representing implicit functions. Using cubic B-spline functions, our positional encoding can achieve \(C^2\) C 2 continuity which is crucial to the quality of reconstruction. To reduce memory usage and speed up convergence, we employ a hash table to store the coefficients of B-spline basis functions; (2) A new loss function integrates data, viscosity, Hessian, and minimal surface terms. Our innovation lies the introduction of the viscosity term, inspired by the vanishing viscosity method, to alleviate the instability in the optimization process and yield a smooth signed distance function solution. To prevent undesired shape variations and ghost geometries, the loss function also incorporates the Hessian term and the minimal surface term. Extensive experimental results demonstrate that our method effectively captures intricate geometric and topological details and outperforms existing reconstruction methods in both quality and accuracy across a diverse range of 3D datasets.