{"slug": "e3dgs-unified-geometric-photometric-equivariance-for-3d-gaussian-splatting-via", "title": "E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding", "summary": "Researchers propose E3DGS, a unified geometric-photometric equivariant architecture for 3D Gaussian Splatting that treats color as a geometric entity via a matrix embedding, achieving SE(3) equivariance without Clebsch-Gordan tensor products. The method, validated on object vision and action-conditioned Gaussian world modeling, demonstrates strong robustness under camera-frame changes and improved data efficiency.", "body_md": "arXiv:2607.15536v1 Announce Type: new\nAbstract: 3D Gaussian Splatting (3DGS) captures scenes by coupling explicit geometry (position, covariance) with view-dependent photometry (Spherical Harmonics). However, building $\\mathrm{SE}(3)$-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: $\\mu\\mapsto R\\mu$, $\\Sigma\\mapsto R\\Sigma R^\\top$, and $f_\\ell\\mapsto D^\\ell(R)f_\\ell$. 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 $\\ell\\le2$, 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 $3\\times3$ matrices. Leveraging this, we introduce the Unified Matrix Embedding, a lifting that maps all Gaussian attributes into a unified carrier space, $\\mathfrak{gl}(3)$. Building on the \"Color-as-Geometry\" formulation, we present E3DGS, a rigid-body ($\\mathrm{SE}(3)$) 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.", "url": "https://wpnews.pro/news/e3dgs-unified-geometric-photometric-equivariance-for-3d-gaussian-splatting-via", "canonical_source": "https://arxiv.org/abs/2607.15536", "published_at": "2026-07-20 04:00:00+00:00", "updated_at": "2026-07-20 13:56:47.649931+00:00", "lang": "en", "topics": ["computer-vision", "machine-learning", "artificial-intelligence", "ai-research"], "entities": ["E3DGS", "3D Gaussian Splatting", "SE(3)"], "alternates": {"html": "https://wpnews.pro/news/e3dgs-unified-geometric-photometric-equivariance-for-3d-gaussian-splatting-via", "markdown": "https://wpnews.pro/news/e3dgs-unified-geometric-photometric-equivariance-for-3d-gaussian-splatting-via.md", "text": "https://wpnews.pro/news/e3dgs-unified-geometric-photometric-equivariance-for-3d-gaussian-splatting-via.txt", "jsonld": "https://wpnews.pro/news/e3dgs-unified-geometric-photometric-equivariance-for-3d-gaussian-splatting-via.jsonld"}}