# Hyperbolic-constraint Point Cloud Reconstruction from Single RGB-D Images

arXiv: https://arxiv.org/abs/2412.09055 · HTML: https://mlsanity.com/paper/2412.09055/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 26 of 26)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation](https://mlsanity.com/paper/2303.13873/) (2023)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2212.04493/) (2022)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)
- [Atlas: End-to-End 3D Scene Reconstruction from Posed Images](https://mlsanity.com/paper/2003.10432/) (2020)
- [Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functions](https://mlsanity.com/paper/2211.13757/) (2022)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [Global-Local Bidirectional Reasoning for Unsupervised Representation Learning of 3D Point Clouds](https://mlsanity.com/paper/2003.12971/) (2020)
- [Multiview Compressive Coding for 3D Reconstruction](https://mlsanity.com/paper/2301.08247/) (2023)
- [USTC-TD: A Test Dataset and Benchmark for Image and Video Coding in 2020s](https://mlsanity.com/paper/2409.08481/) (2024)
- [CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data](https://mlsanity.com/paper/2111.15037/) (2021)
- [Rethinking the compositionality of point clouds through regularization in the hyperbolic space](https://mlsanity.com/paper/2209.10318/) (2022)
- [Offline and Online Optical Flow Enhancement for Deep Video Compression](https://mlsanity.com/paper/2307.05092/) (2023)
- [NU-MCC: Multiview Compressive Coding with Neighborhood Decoder and Repulsive UDF](https://mlsanity.com/paper/2307.09112/) (2023)
- [Registered and Segmented Deformable Object Reconstruction from a Single View Point Cloud](https://mlsanity.com/paper/2311.07357/) (2023)

## Built on by (most cited first, 8 of 8)

- [Modality Alignment across Trees on Heterogeneous Hyperbolic Manifolds](https://mlsanity.com/paper/2510.27391/) (2025)
- [HyPCV-Former: Hyperbolic Spatio-Temporal Transformer for 3D Point Cloud Video Anomaly Detection](https://mlsanity.com/paper/2508.00473/) (2025)
- [Quaternion Approximation Networks for Enhanced Image Classification and Oriented Object Detection](https://mlsanity.com/paper/2509.05512/) (2025)
- [RoamScene3D: Immersive Text-to-3D Scene Generation via Adaptive Object-aware Roaming](https://mlsanity.com/paper/2601.19433/) (2026)
- [Hierarchical Semantic-Constrained Heterogeneous Graph for Audio-Visual Event Localization](https://mlsanity.com/paper/2606.07033/) (2026)
- [Mamba Learns in Context: Structure-Aware Domain Generalization for Multi-Task Point Cloud Understanding](https://mlsanity.com/paper/2603.20739/) (2026)
- [Hyperbolic Distillation: Geometry-Guided Cross-Modal Transfer for Robust 3D Object Detection](https://mlsanity.com/paper/2605.09899/) (2026)
- [Learning Taxonomic Trees with Hierarchical Representation Regularization for Large Multimodal Models](https://mlsanity.com/paper/2607.02909/) (2026)

## Abstract (arXiv)

Reconstructing desired objects and scenes has long been a primary goal in 3D computer vision. Single-view point cloud reconstruction has become a popular technique due to its low cost and accurate results. However, single-view reconstruction methods often rely on expensive CAD models and complex geometric priors. Effectively utilizing prior knowledge about the data remains a challenge. In this paper, we introduce hyperbolic space to 3D point cloud reconstruction, enabling the model to represent and understand complex hierarchical structures in point clouds with low distortion. We build upon previous methods by proposing a hyperbolic Chamfer distance and a regularized triplet loss to enhance the relationship between partial and complete point clouds. Additionally, we design adaptive boundary conditions to improve the model's understanding and reconstruction of 3D structures. Our model outperforms most existing models, and ablation studies demonstrate the significance of our model and its components. Experimental results show that our method significantly improves feature extraction capabilities. Our model achieves outstanding performance in 3D reconstruction tasks.