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

TL;DR

This work addresses single-view 3D point cloud reconstruction by mitigating reliance on CAD priors and improving the modeling of hierarchical, tree-like structures. It introduces HcPCR, which embeds partial and complete point-cloud features into a hyperbolic space using the Poincaré ball, and it defines a HyperCD distance to guide matching in this non-Euclidean geometry. The method combines a hyperbolic regularization loss with an adaptive margin and a hyperbolic triplet loss, producing an overall loss $\mathcal{L} = \mathcal{L}_N + \mathcal{L}_Z + \mathcal{L}_T$ that enhances part–whole relationships. Empirical results on CO3D-v2 show consistent improvements over baselines across multiple metrics, with ablations highlighting the importance of adaptive margins, curvature selection, and hyperbolic representations for capturing hierarchy and improving reconstruction quality.

Abstract

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.

Figures (6)

• Figure 1: This figure illustrates the efficient embedding of a tree structure from Euclidean space into hyperbolic space. The left side depicts a multi-level tree structure in Euclidean space, while the right side shows the projection of hyperbolic space. Nodes of different colors represent various categories. In hyperbolic space, the node distribution more accurately reflects their hierarchical relationships.
• Figure 2: Architecture of the HcPCR. To enhance the understanding of the hierarchical structure of the point clouds, we embed both partial and complete features into a hyperbolic space. The lower-level features (partial point cloud) are embedded into the lower-dimensional central region, while the higher-level features (complete point cloud) are distributed in the higher-dimensional peripheral region. Additionally, a triplet loss is utilized to push apart point clouds of different categories and to pull together point clouds with similar attributes.
• Figure 3: Visualisation comparison on CO3D-v2 validation set. We have selected three categories. Each category contained two samples for evaluation.
• Figure 4: Ablation Study of different margin and curvature.
• Figure 5: Visualisation results of ablation study with (w) or without (w/o) the full loss function.