E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding
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: $μ\mapsto Rμ$, $Σ\mapsto RΣR^\top$, and $f_\ell\mapsto D^\ell(R)f_\ell$. This mismatch complicates strict equivariance, leading existing method...
| Authors | Chankyo Kim, Maani Ghaffari |
|---|---|
| Primary category | cs.CV |
| Published | 17 July 2026 |
| Last updated at source | 17 July 2026 |
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