3D Gaussian Splatting (3DGS) captures scenes by coupling explicit geometry (position, covariance) with view-dependent photometry (Spherical Harmonics). However, building SE(3)-equivariant architectures on these primitives presents a fundamental representation bottleneck. Color has been treated as a signal rather than a geometric entity, making it nontrivial to unify symmetry across geometry and appearance as the camera frame changes. While translations are handled by relative coordinates, rotations act heterogeneously across attributes: μ↦Rμ, Σ↦RΣR⊤, and fℓ↦Dℓ(R)fℓ. This mismatch complicates strict equivariance, leading existing methods to either discard or flatten SH coefficients, thereby breaking symmetry. We propose a unified solution rooted in representation theory: for SH degrees ℓ≤2, photometry is algebraically isomorphic to a rank-2 geometric tensor. We prove that the Wigner-D action on these SH coefficients can be exactly reformulated as the conjugation action on 3×3 matrices. Leveraging this, we introduce the Unified Matrix Embedding, a lifting that maps all Gaussian attributes into a unified carrier space, gl(3). Building on the "Color-as-Geometry" formulation, we present E3DGS, a rigid-body (SE(3)) equivariant architecture that processes 3D Gaussians without Clebsch-Gordan tensor products. Evaluations on object vision and action-conditioned Gaussian world modeling demonstrate that our unified approach yields strong robustness under camera-frame changes and improved data efficiency.
In this paper, we present a novel geometry-aware style transfer framework for 3D Gaussian splatting (3DGS) that simultaneously transfers appearance attributes and geometric structures. Unlike prior works that primarily focus on color-based stylization and often overlook structural adaptation, our method explicitly incorporates geometry adaptation through a decoupled optimization scheme that alternately updates color and geometry parameters. This strategy alleviates potential interference between color and geometry updates, leading to stable and consistent scene-level geometry transformation. The decoupled optimization is enabled by the proposed geometry-aware contrastive feature matching (GCFM). GCFM integrates RGB, depth, and edge cues into a contrastive objective and is employed in both optimization phases to effectively transfer structural characteristics from style images to Gaussian primitives. Extensive experiments show that our approach achieves superior performance in both qualitative fidelity and quantitative metrics, significantly outperforming existing 3DGS-based stylization methods. Our code is available at \href{https://github.com/oweixx/gast}{https://github.com/oweixx/gast}.
3D Gaussian Splatting (3DGS) has been widely adopted for scene reconstruction, where training inherently constitutes a highly coupled and non-convex optimization problem. Recent works commonly incorporate geometric priors, such as LiDAR measurements, either for initialization or as training constraints, with the goal of improving photometric reconstruction quality. However, in large-scale outdoor scenarios, such geometric supervision is often spatially incomplete and uneven, which limits its effectiveness as a reliable prior and can even be detrimental to the final reconstruction. To address this challenge, we model partially observable geometry as a continuous energy field induced by geometric evidence and propose EnerGS. Rather than enforcing geometry as a hard constraint, EnerGS provides a soft geometric guidance for the optimization of Gaussian primitives, allowing geometric information to steer the optimization process without directly restricting the solution space. Extensive experiments on large-scale outdoor scenes demonstrate that, under both sparse multi-view and monocular settings, EnerGS consistently improves photometric quality and geometric stability, while effectively mitigating overfitting during 3DGS training.
3D Gaussian Splatting (3DGS) is a recent approach for scene rendering. Although primarily designed for view synthesis, its potential for scene understanding tasks remains underexplored. In this work, we conduct a comparative evaluation of various geometric deep learning architectures for the classification of 3D scenes represented using Gaussian Splatting. We benchmark point-based and graph-based models across both traditional point cloud datasets and dedicated Gaussian Splatting datasets. Scenes are embedded into latent representations, which are evaluated through end-to-end classification, linear probing, and clustering analysis. Our study provides insight into the suitability of different geometry-aware architectures and input feature configurations for learning effective 3D Gaussian Splat representations. The results highlight consistent differences between architectural families and reveal the impact of Gaussian-specific attributes on the quality of representation.
Julia Farganus, Krzysztof Żurawicki, Arkadiusz Gaweł +2