# Preserving Topological and Geometric Embeddings for Point Cloud Recovery

arXiv: https://arxiv.org/abs/2507.19121 · HTML: https://mlsanity.com/paper/2507.19121/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 54 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 30 of 36)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [PMP-Net: Point Cloud Completion by Learning Multi-step Point Moving Paths](https://mlsanity.com/paper/2012.03408/) (2020)
- [SeedFormer: Patch Seeds based Point Cloud Completion with Upsample Transformer](https://mlsanity.com/paper/2207.10315/) (2022)
- [SCPNet: Semantic Scene Completion on Point Cloud](https://mlsanity.com/paper/2303.06884/) (2023)
- [SampleNet: Differentiable Point Cloud Sampling](https://mlsanity.com/paper/1912.03663/) (2019)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021)
- [ProxyFormer: Proxy Alignment Assisted Point Cloud Completion with Missing Part Sensitive Transformer](https://mlsanity.com/paper/2302.14435/) (2023)
- [Grad-PU: Arbitrary-Scale Point Cloud Upsampling via Gradient Descent with Learned Distance Functions](https://mlsanity.com/paper/2304.11846/) (2023)
- [Attention-based Point Cloud Edge Sampling](https://mlsanity.com/paper/2302.14673/) (2023)
- [Meta-PU: An Arbitrary-Scale Upsampling Network for Point Cloud](https://mlsanity.com/paper/2102.04317/) (2021)
- [SVDFormer: Complementing Point Cloud via Self-view Augmentation and Self-structure Dual-generator](https://mlsanity.com/paper/2307.08492/) (2023)
- [PU-Transformer: Point Cloud Upsampling Transformer](https://mlsanity.com/paper/2111.12242/) (2021)

## Abstract (arXiv)

Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture named TopGeoFormer, which maintains these critical properties throughout the sampling and restoration phases. First, we revisit traditional feature extraction techniques to yield topological embedding using a continuous mapping of relative relationships between neighboring points, and integrate it in both phases for preserving the structure of the original space. Second, we propose the InterTwining Attention to fully merge topological and geometric embeddings, which queries shape with local awareness in both phases to form a learnable 3D shape context facilitated with point-wise, point-shape-wise, and intra-shape features. Third, we introduce a full geometry loss and a topological constraint loss to optimize the embeddings in both Euclidean and topological spaces. The geometry loss uses inconsistent matching between coarse-to-fine generations and targets for reconstructing better geometric details, and the constraint loss limits embedding variances for better approximation of the topological space. In experiments, we comprehensively analyze the circumstances using the conventional and learning-based sampling/upsampling/recovery algorithms. The quantitative and qualitative results demonstrate that our method significantly outperforms existing sampling and recovery methods.