# A PCA Based Model for Surface Reconstruction from Incomplete Point Clouds

arXiv: https://arxiv.org/abs/2509.15675 · HTML: https://mlsanity.com/paper/2509.15675/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Curvature Regularized Surface Reconstruction from Point Cloud](https://mlsanity.com/paper/2001.07884/) (2020)
- [A Color Elastica Model for Vector-Valued Image Regularization](https://mlsanity.com/paper/2008.08255/) (2020)
- [An Operator-Splitting Method for the Gaussian Curvature Regularization Model with Applications to Surface Smoothing and Imaging](https://mlsanity.com/paper/2108.01914/) (2021)
- [Euler's Elastica Based Cartoon-Smooth-Texture Image Decomposition](https://mlsanity.com/paper/2407.02794/) (2024)
- [Triangulated Surface Denoising using High Order Regularization with Dynamic Weights](https://mlsanity.com/paper/1711.08137/) (2017)
- [An efficient iterative method for reconstructing surface from point clouds](https://mlsanity.com/paper/2005.11864/) (2020)
- [Fast Algorithms for Surface Reconstruction from Point Cloud](https://mlsanity.com/paper/1907.01142/) (2019)

## Abstract (arXiv)

Point cloud data represents a crucial category of information for mathematical modeling, and surface reconstruction from such data is an important task across various disciplines. However, during the scanning process, the collected point cloud data may fail to cover the entire surface due to factors such as high light-absorption rate and occlusions, resulting in incomplete datasets. Inferring surface structures in data-missing regions and successfully reconstructing the surface poses a challenge. In this paper, we present a Principal Component Analysis (PCA) based model for surface reconstruction from incomplete point cloud data. Initially, we employ PCA to estimate the normal information of the underlying surface from the available point cloud data. This estimated normal information serves as a regularizer in our model, guiding the reconstruction of the surface, particularly in areas with missing data. Additionally, we introduce an operator-splitting method to effectively solve the proposed model. Through systematic experimentation, we demonstrate that our model successfully infers surface structures in data-missing regions and well reconstructs the underlying surfaces, outperforming existing methodologies.