A Thresholding Based Operator-Splitting Method for Curvature-Regularized Surface Reconstruction
Abstract
Surface reconstruction from point clouds is a fundamental problem in computational geometry with broad applications in computer graphics, medical imaging, and manufacturing. In this paper, we propose an efficient method for solving a curvature-regularized surface reconstruction model. To avoid the computational cost associated with reinitialization in traditional level set methods, we represent the reconstructed surface by an indicator function. By introducing an auxiliary variable, we reformulate the original optimization problem as the computation of the steady-state solution of an initial value problem. We then develop an operator-splitting method to decompose the resulting problem into two tractable subproblems, one of which can be efficiently solved by iterative thresholding. The proposed approach combines the advantages of curvature regularization, operator splitting, and threshold dynamics. Numerical experiments show that the proposed method is computationally efficient and can accurately reconstruct sharp corners and concave features.
Related
- Curvature growth and holomorphic splitting for Kähler metrics with cone singularities
- A new operator splitting method for coupled PDE problems, with an application to poromechanics
- Operator Splitting Methods with Online Scaling
- Almost-splitting of spacetimes under timelike sectional curvature bounds
- Regularized-Likelihood Deconvolution with Posterior-Density Reconstruction
BibTeX
@misc{hu2026thresholding,
title = {{A Thresholding Based Operator-Splitting Method for Curvature-Regularized Surface Reconstruction}},
author = {Yang Hu and Hao Liu and Dong Wang and Tieyong Zeng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.29584},
eprint = {2607.29584},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.29584},
}
RIS
TY - UNPB
TI - A Thresholding Based Operator-Splitting Method for Curvature-Regularized Surface Reconstruction
AU - Yang Hu
AU - Hao Liu
AU - Dong Wang
AU - Tieyong Zeng
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2607.29584
UR - https://arxiv.org/abs/2607.29584
AB - Surface reconstruction from point clouds is a fundamental problem in computational geometry with broad applications in computer graphics, medical imaging, and manufacturing. In this paper, we propose an efficient method for solving a curvature-regularized surface reconstruction model. To avoid the computational cost associated with reinitialization in traditional level set methods, we represent the reconstructed surface by an indicator function. By introducing an auxiliary variable, we reformulate the original optimization problem as the computation of the steady-state solution of an initial value problem. We then develop an operator-splitting method to decompose the resulting problem into two tractable subproblems, one of which can be efficiently solved by iterative thresholding. The proposed approach combines the advantages of curvature regularization, operator splitting, and threshold dynamics. Numerical experiments show that the proposed method is computationally efficient and can accurately reconstruct sharp corners and concave features.
ER -