# Manifold-Aware Point Cloud Completion via Geodesic-Attentive Hierarchical Feature Learning

arXiv: https://arxiv.org/abs/2512.05710 · HTML: https://mlsanity.com/paper/2512.05710/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [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)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Variational Relational Point Completion Network](https://mlsanity.com/paper/2104.10154/) (2021)
- [SeedFormer: Patch Seeds based Point Cloud Completion with Upsample Transformer](https://mlsanity.com/paper/2207.10315/) (2022)
- [AdaPoinTr: Diverse Point Cloud Completion with Adaptive Geometry-Aware Transformers](https://mlsanity.com/paper/2301.04545/) (2023)
- [PointAttN: You Only Need Attention for Point Cloud Completion](https://mlsanity.com/paper/2203.08485/) (2022)
- [CRA-PCN: Point Cloud Completion with Intra- and Inter-level Cross-Resolution Transformers](https://mlsanity.com/paper/2401.01552/) (2024)
- [SymmCompletion: High-Fidelity and High-Consistency Point Cloud Completion with Symmetry Guidance](https://mlsanity.com/paper/2503.18007/) (2025)
- [PointSea: Point Cloud Completion via Self-structure Augmentation](https://mlsanity.com/paper/2502.17053/) (2025)
- [PointCFormer: a Relation-based Progressive Feature Extraction Network for Point Cloud Completion](https://mlsanity.com/paper/2412.08421/) (2024)
- [Position-aware Guided Point Cloud Completion with CLIP Model](https://mlsanity.com/paper/2412.08271/) (2024)

## Abstract (arXiv)

Point cloud completion seeks to recover geometrically consistent shapes from partial or sparse 3D observations. Although recent methods have achieved reasonable global shape reconstruction, they often rely on Euclidean proximity and overlook the intrinsic nonlinear geometric structure of point clouds, resulting in suboptimal geometric consistency and semantic ambiguity. In this paper, we present a manifold-aware point cloud completion framework that explicitly incorporates nonlinear geometry information throughout the feature learning pipeline. Our approach introduces two key modules: a Geodesic Distance Approximator (GDA), which estimates geodesic distances between points to capture the latent manifold topology, and a Manifold-Aware Feature Extractor (MAFE), which utilizes geodesic-based k-NN groupings and a geodesic-relational attention mechanism to guide the hierarchical feature extraction process. By integrating geodesic-aware relational attention, our method promotes semantic coherence and structural fidelity in the reconstructed point clouds. Extensive experiments on benchmark datasets demonstrate that our approach consistently outperforms state-of-the-art methods in reconstruction quality.