# Topology-Aware Surface Reconstruction for Point Clouds

arXiv: https://arxiv.org/abs/1811.12543 · HTML: https://mlsanity.com/paper/1811.12543/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2018.

## Built on by (most cited first, 22 of 22)

- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide](https://mlsanity.com/paper/2105.07025/) (2021)
- [A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis](https://mlsanity.com/paper/2109.00530/) (2021)
- [Topological Node2vec: Enhanced Graph Embedding via Persistent Homology](https://mlsanity.com/paper/2309.08241/) (2023)
- [4DRecons: 4D Neural Implicit Deformable Objects Reconstruction from a single RGB-D Camera with Geometrical and Topological Regularizations](https://mlsanity.com/paper/2406.10167/) (2024)
- [Revisiting Point Cloud Completion: Are We Ready For The Real-World?](https://mlsanity.com/paper/2411.17580/) (2024)
- [A Practical Solver for Scalar Data Topological Simplification](https://mlsanity.com/paper/2407.12399/) (2024)
- [Optimisation of Spectral Wavelets for Persistence-based Graph Classification](https://mlsanity.com/paper/2101.05201/) (2021)
- [Domain Adaptation by Topology Regularization](https://mlsanity.com/paper/2101.12102/) (2021)
- [GLiDR: Topologically Regularized Graph Generative Network for Sparse LiDAR Point Clouds](https://mlsanity.com/paper/2312.00068/) (2023)
- [Tight basis cycle representatives for persistent homology of large data sets](https://mlsanity.com/paper/2206.02925/) (2022)
- [Filtration learning in exact multi-parameter persistent homology and classification of time-series data](https://mlsanity.com/paper/2406.19587/) (2024)
- [Topology Aware Neural Interpolation of Scalar Fields](https://mlsanity.com/paper/2508.17995/) (2025)
- [Topological Regularization for Dense Prediction](https://mlsanity.com/paper/2111.10984/) (2021)
- [Learning Polynomial Representations of Physical Objects with Application to Certifying Correct Packing Configurations](https://mlsanity.com/paper/2312.06791/) (2023)
- [Persistence kernels for classification: A comparative study](https://mlsanity.com/paper/2408.07090/) (2024)
- [Curvy: A Parametric Cross-section based Surface Reconstruction](https://mlsanity.com/paper/2409.00829/) (2024)
- [TUN: Detecting Significant Points in Persistence Diagrams with Deep Learning](https://mlsanity.com/paper/2512.14274/) (2025)
- [Filmsticking++: Rapid Film Sticking for Explicit Surface Reconstruction](https://mlsanity.com/paper/2602.11433/) (2026)
- [Non-negative Matrix Factorisation with Topological Regularisation](https://mlsanity.com/paper/2606.17531/) (2026)

## Abstract (arXiv)

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated in the optimization algorithm promote the correct topology. The result is a novel topology-aware technique which can: 1.) weed out topological noise from point scans, and 2.) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We showcase results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data.