Related papers: E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding

E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding

URL: http://arxiv.org/abs/2607.15536v1
Date: Fri, 17 Jul 2026 01:12:26 GMT
Title: E3DGS: Unified Geometric-Photometric Equivariance for 3D Gaussian Splatting via Color-as-Geometry Embedding
Abstract summary: 3D Gaussian Splatting (3DGS) captures scenes by coupling explicit geometry with view-dependent photometry (Spherical Harmonics)<n>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.<n>We present E3DGS, a rigid-body ($mathrmSE(3)$)variant architecture that processes 3D Gaussians without Clebsch-Gordan tensor products.
Score: 9.35652906982887
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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 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.

Related papers

Stable and Scalable Bundle Adjustment of Holistic 3D Structures [99.03818732955783]
We present a new version of Bundle Adjustment (BA) for 3D computer vision.<n>BA is developed to jointly optimize cameras, poses and 3D points.<n>By group-induced measurements and cross-feature reprojection, we preserve the sparsity of classical point-only 3D regularization.
arXiv Detail & Related papers (2026-09-03T16:08:03Z)
EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs [12.013314817711054]
We introduce EqGINO, a geometrically robust framework that enforces isotropy in the spectral domain.<n>Our method robustly models coordinate-invariant physical laws on complex irregular 3D geometries.
arXiv Detail & Related papers (2026-06-02T07:23:06Z)
G2P: Gaussian-to-Point Attribute Alignment for Boundary-Aware 3D Semantic Segmentation [22.750868489199686]
We propose Gaussian-to-Point (G2P), which transfers appearance-aware attributes from 3D Gaussian Splatting to point clouds for more discriminative and appearance-consistent segmentation.<n>Our approach achieves superior performance on standard benchmarks and shows significant improvements on geometrically challenging classes, all without any 2D or language supervision.
arXiv Detail & Related papers (2026-01-07T01:44:29Z)
GaussianMorphing: Mesh-Guided 3D Gaussians for Semantic-Aware Object Morphing [31.47036497656664]
We introduce a novel framework for semantic-aware 3D shape and texture morphing from multi-view images.<n>The core of our framework is a unified deformation strategy that anchors 3DGaussians to reconstructed mesh patches.<n>On our proposed TexMorph benchmark, GaussianMorphing substantially outperforms prior 2D/3D methods.
arXiv Detail & Related papers (2025-10-02T14:07:55Z)
GaussRender: Learning 3D Occupancy with Gaussian Rendering [86.89653628311565]
GaussRender is a module that improves 3D occupancy learning by enforcing projective consistency.<n>Our method penalizes 3D configurations that produce inconsistent 2D projections, thereby enforcing a more coherent 3D structure.
arXiv Detail & Related papers (2025-02-07T16:07:51Z)
Self-Ensembling Gaussian Splatting for Few-Shot Novel View Synthesis [55.561961365113554]
3D Gaussian Splatting (3DGS) has demonstrated remarkable effectiveness in novel view synthesis (NVS)<n>In this paper, we introduce Self-Ensembling Gaussian Splatting (SE-GS)<n>We achieve self-ensembling by incorporating an uncertainty-aware perturbation strategy during training.<n> Experimental results on the LLFF, Mip-NeRF360, DTU, and MVImgNet datasets demonstrate that our approach enhances NVS quality under few-shot training conditions.
arXiv Detail & Related papers (2024-10-31T18:43:48Z)
Effective Rank Analysis and Regularization for Enhanced 3D Gaussian Splatting [33.01987451251659]
3D Gaussian Splatting (3DGS) has emerged as a promising technique capable of real-time rendering with high-quality 3D reconstruction.<n>Despite its potential, 3DGS encounters challenges such as needle-like artifacts, suboptimal geometries, and inaccurate normals.<n>We introduce the effective rank as a regularization, which constrains the structure of the Gaussians.
arXiv Detail & Related papers (2024-06-17T15:51:59Z)
Trim 3D Gaussian Splatting for Accurate Geometry Representation [72.00970038074493]
We introduce Trim 3D Gaussian Splatting (TrimGS) to reconstruct accurate 3D geometry from images. Our experimental and theoretical analyses reveal that a relatively small Gaussian scale is a non-negligible factor in representing and optimizing the intricate details. When combined with the original 3DGS and the state-of-the-art 2DGS, TrimGS consistently yields more accurate geometry and higher perceptual quality.
arXiv Detail & Related papers (2024-06-11T17:34:46Z)
GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction [70.65250036489128]
3D semantic occupancy prediction aims to obtain 3D fine-grained geometry and semantics of the surrounding scene. We propose an object-centric representation to describe 3D scenes with sparse 3D semantic Gaussians. GaussianFormer achieves comparable performance with state-of-the-art methods with only 17.8% - 24.8% of their memory consumption.
arXiv Detail & Related papers (2024-05-27T17:59:51Z)
3D Geometry-aware Deformable Gaussian Splatting for Dynamic View Synthesis [49.352765055181436]
We propose a 3D geometry-aware deformable Gaussian Splatting method for dynamic view synthesis. Our solution achieves 3D geometry-aware deformation modeling, which enables improved dynamic view synthesis and 3D dynamic reconstruction.
arXiv Detail & Related papers (2024-04-09T12:47:30Z)
Gaussian Grouping: Segment and Edit Anything in 3D Scenes [65.49196142146292]
We propose Gaussian Grouping, which extends Gaussian Splatting to jointly reconstruct and segment anything in open-world 3D scenes. Compared to the implicit NeRF representation, we show that the grouped 3D Gaussians can reconstruct, segment and edit anything in 3D with high visual quality, fine granularity and efficiency.
arXiv Detail & Related papers (2023-12-01T17:09:31Z)
Rotation Equivariant 3D Hand Mesh Generation from a Single RGB Image [1.8692254863855962]
We develop a rotation equivariant model for generating 3D hand meshes from 2D RGB images. This guarantees that as the input image of a hand is rotated the generated mesh undergoes a corresponding rotation.
arXiv Detail & Related papers (2021-11-25T11:07:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.