Joint Orientation and Weight Optimization for Robust Watertight Surface Reconstruction via Dirichlet-Regularized Winding Fields

2026-02-14

AI Summary

This work proposes a robust watertight surface reconstruction method for unoriented, non-uniformly sampled point clouds corrupted by noise and outliers. The approach uniquely integrates the joint optimization of point normals, area weights, and confidence coefficients within a unified framework, constructing an implicit representation based on the generalized winding number field. Smoothness is enforced through Dirichlet energy minimization, providing effective regularization without requiring any preprocessing to handle complex point cloud defects. Experimental results demonstrate that the method consistently produces high-quality watertight surfaces from challenging inputs, including outputs from 3D Gaussian Splatting and corrupted geometry benchmarks, outperforming both conventional multi-stage pipelines and existing joint reconstruction techniques.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We propose Dirichlet Winding Reconstruction (DiWR), a robust method for reconstructing watertight surfaces from unoriented point clouds with non-uniform sampling, noise, and outliers. Our method uses the generalized winding number (GWN) field as the target implicit representation and jointly optimizes point orientations, per-point area weights, and confidence coefficients in a single pipeline. The optimization minimizes the Dirichlet energy of the induced winding field together with additional GWN-based constraints, allowing DiWR to compensate for non-uniform sampling, reduce the impact of noise, and downweight outliers during reconstruction, with no reliance on separate preprocessing. We evaluate DiWR on point clouds from 3D Gaussian Splatting, a computer-vision pipeline, and corrupted graphics benchmarks. Experiments show that DiWR produces plausible watertight surfaces on these challenging inputs and outperforms both traditional multi-stage pipelines and recent joint orientation-reconstruction methods.

Problem

• watertight surface reconstruction
• unoriented point clouds
• non-uniform sampling
• noise
• outliers

Innovation

• Dirichlet energy
• winding number field
• joint optimization
• watertight reconstruction
• unoriented point clouds