# An efficient iterative method for reconstructing surface from point clouds

arXiv: https://arxiv.org/abs/2005.11864 · HTML: https://mlsanity.com/paper/2005.11864/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2020.

## Built on by (most cited first, 3 of 3)

- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks](https://mlsanity.com/paper/2307.09039/) (2023)
- [A PCA Based Model for Surface Reconstruction from Incomplete Point Clouds](https://mlsanity.com/paper/2509.15675/) (2025)

## Abstract (arXiv)

Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The surface is implicitly represented by indicator functions and the energy functional is then approximated based on such representations using heat kernel convolutions. We then develop a novel iterative method to minimize the approximate energy and prove the energy decaying property during each iteration. We then use asymptotic expansion to give a connection between the proposed algorithm and active contour models. Extensive numerical experiments are performed in both 2- and 3- dimensional Euclidean spaces to show that the proposed method is simple, efficient, and accurate.