A dataset-free approach for self-supervised learning of 3D reflectional symmetries

TL;DR

This work tackles 3D reflectional symmetry detection without dataset-dependent supervision by leveraging self-priors derived from a single object. It constructs per-point visual features by back-projecting image-model descriptors from Fibonacci-distributed viewpoints and couples them with a PointNet-based symmetry generator trained with an extended Chamfer loss that incorporates both geometry and features. The model predicts up to three reflective planes via Householder transformations, optimized over $L = L_{congruence} + L_{reg}$, and evaluated on ShapeNet where it outperforms trained baselines and maintains robustness to unseen geometries. The findings demonstrate strong generalization, efficiency, and improved precision at small angular errors, with promising avenues for extending to rotation symmetries and real-time applications in graphics and cultural heritage contexts.

Abstract

In this paper, we explore a self-supervised model that learns to detect the symmetry of a single object without requiring a dataset-relying solely on the input object itself. We hypothesize that the symmetry of an object can be determined by its intrinsic features, eliminating the need for large datasets during training. Additionally, we design a self-supervised learning strategy that removes the necessity of ground truth labels. These two key elements make our approach both effective and efficient, addressing the prohibitive costs associated with constructing large, labeled datasets for this task. The novelty of our method lies in computing features for each point on the object based on the idea that symmetric points should exhibit similar visual appearances. To achieve this, we leverage features extracted from a foundational image model to compute a visual descriptor for the points. This approach equips the point cloud with visual features that facilitate the optimization of our self-supervised model. Experimental results demonstrate that our method surpasses the state-of-the-art models trained on large datasets. Furthermore, our model is more efficient, effective, and operates with minimal computational and data resources.

Figures (7)

• Figure 1: The figure shows the detected symmetries along with the overlapping point clouds (original and symmetric) for two examples of the Thingi10K dataset. Our method converges in very few iterations, which makes it very efficient in practice.
• Figure 2: A symmetry generator looks at the input point cloud $\mathcal{O}$ and predicts a transformation $T_{\Phi}$ to apply to $\mathcal{O}$. A modified Chamfer Loss is carried out between $\mathcal{O}$, $T_{\Phi}(\mathcal{O})$ and the features $\mathcal{F}$. The model is trained to determine $T_\Phi$ such that $\mathcal{O}$ and $T_\Phi(\mathcal{O})$ correspond symmetrically. The expected output of the model is $T_\Phi$.
• Figure 3: Left: uniform and Fibonacci sampling on a sphere. Right: Plot of features as colors. Note the symmetric consistency of the features.
• Figure 4: Examples of symmetries detected with our method.
• Figure 5: Out-of-distribution evaluation. From top to bottom: detected symmetries from methods Diffusion, E3Sym, and our method. Note: Diffusion does not detect symmetries for the dragon.

Theorems & Definitions (2)

• Definition 1
• Definition 2