GeoGS: Geometry-only Gaussian Splatting

• GeoGS is a framework where Gaussian primitives are optimized for geometry rather than appearance, focusing on accurate surface reconstruction and depth fidelity.
• Different formulations of GeoGS decouple or remove color parameters, using techniques like depth-normal regularization and curvature alignment to enforce geometric consistency.
• Empirical studies demonstrate that GeoGS improves reconstruction metrics and reduces computational overhead across applications like panoramas, dynamics, and SLAM.

Geometry-only Gaussian Splatting (GeoGS) denotes a geometry-centric strand of Gaussian-splatting research in which Gaussian primitives are optimized primarily for surface reconstruction, depth fidelity, normal consistency, or map quality rather than for appearance alone. The recent literature suggests that the label does not identify a single canonical method. Instead, it covers several related formulations: strictly geometry-only representations that remove color parameters, hybrid systems that decouple geometry from appearance, and geometry-focused variants of 3DGS that still retain photometric rendering terms while making geometric consistency the central training signal (Zhou et al., 8 Jul 2026, Zhou et al., 3 Jun 2026, Yao et al., 5 Jan 2026, Jiang et al., 2024).

1. Terminology and conceptual scope

In the cited literature, “GeoGS” is used in several technically distinct but related senses. Some works use it literally, as a representation with no appearance modeling; others use it to denote geometry-first optimization inside an otherwise standard Gaussian-splatting renderer.

Paper	Meaning of GeoGS	Defining mechanism
"360-GeoGS: Geometrically Consistent Feed-Forward 3D Gaussian Splatting Reconstruction for 360 Images" (Yao et al., 5 Jan 2026)	Geometry-focused feed-forward 3DGS for panoramas	Depth-Normal regularization on Gaussian position, rotation, and scale
"Geometry Field Splatting with Gaussian Surfels" (Jiang et al., 2024)	Geometry-only splatting of a geometry field	Gaussian surfels splat $F(\mathbf{x})$ rather than volumetric density
"Decoupling Motion and Geometry in 4D Gaussian Splatting" (Zhang et al., 1 Mar 2026)	GeoGS mode inside 4DGS	Set $v(t)=0$ and disable GDN for time-invariant geometry
"Geometry Gaussians: Decoupling Appearance and Geometry in Gaussian Splatting" (Zhou et al., 3 Jun 2026)	Geometry-only behavior via decoupled opacity	Separate $\mathrm{opacity}_{color}$ and $\mathrm{opacity}_{geo}$
"GeoGS-SLAM: Geometry-Only Gaussian Splatting for Dense Monocular SLAM" (Zhou et al., 8 Jul 2026)	Strict geometry-only Gaussian map for SLAM	Remove SH/color and keep only spatial parameters

Adjacent work broadens the same design space even when it does not use the exact label. "GeoGaussian: Geometry-aware Gaussian Splatting for Scene Rendering" (Li et al., 2024) preserves geometry through thin surface-aligned ellipsoids, co-planarity losses, and tangent-plane densification. "GeoSplat: A Deep Dive into Geometry-Constrained Gaussian Splatting" (Li et al., 5 Sep 2025) extends this idea by using first-order and second-order geometric quantities, including principal curvatures and directions, throughout initialization, gradient updates, and densification. "Geometry-Grounded Gaussian Splatting" (Zhang et al., 25 Jan 2026) provides a stochastic-solid interpretation of Gaussian primitives and uses physically grounded volumetric depth for shape extraction. "Sparse2DGS: Geometry-Prioritized Gaussian Splatting for Surface Reconstruction from Sparse Views" (Wu et al., 29 Apr 2025) freezes appearance and shifts optimization toward geometry-expressive feature supervision under sparse views.

A common misconception is that every GeoGS system is appearance-free. The most explicit counterexample is 360-GeoGS, which states that it is “not strictly ‘geometry-only’ in the sense of ignoring appearance”; it still learns colors via spherical harmonics and includes a photometric loss, while adding strong geometric regularization on Gaussian position, scale, and rotation (Yao et al., 5 Jan 2026). Conversely, GeoGS-SLAM is explicitly geometry-only: it removes all appearance modeling and keeps only spatial parameters, reducing per-primitive parameters from $59$ to $10$, a reduction of approximately $83.1\%$ (Zhou et al., 8 Jul 2026).

2. Representational foundations

Most GeoGS formulations inherit the basic 3DGS parameterization of a primitive by center, orientation, anisotropic scale, covariance, and opacity. In 360-GeoGS, a 3D Gaussian primitive has mean $\mu \in \mathbb{R}^3$, rotation $R \in SO(3)$, scales $\mathbf{s}=(s_1,s_2,s_3)^\top$, covariance

$v(t)=0$0

opacity $v(t)=0$1, and appearance coefficients $v(t)=0$2 represented by spherical harmonics. Projection uses the Jacobian of the camera mapping, giving the induced image-space covariance

$v(t)=0$3

This is standard GS structure, but GeoGS-style methods reinterpret which parameters carry geometry and how they should be constrained (Yao et al., 5 Jan 2026).

A first major branch treats geometry as a surface-aligned anisotropic primitive. GeoGaussian initializes thin ellipsoids aligned with surface normals, fixes the thickness scale along the normal to a small constant such as $v(t)=0$4 for smoothly connected regions, and constrains densification to tangent planes so that new Gaussians remain co-planar with local surfaces (Li et al., 2024). GeoSplat pushes this further by aligning Gaussian axes to principal curvature directions and setting tangent-plane scales from curvature ratios, while keeping the normal-axis scale near $v(t)=0$5 so that the primitive behaves as a surface-hugging “pancake” (Li et al., 5 Sep 2025). Sparse2DGS adopts 2DGS-style planar disk Gaussians with two tangent directions, a derived normal $v(t)=0$6, and a scale matrix $v(t)=0$7, making the primitive intrinsically surface-like rather than volumetric (Wu et al., 29 Apr 2025). GeoGS-SLAM uses the same geometry-only intuition at the SLAM level by parameterizing each primitive as

$v(t)=0$8

with planar scale and no color or SH coefficients (Zhou et al., 8 Jul 2026).

A second branch treats geometry as a field rather than as a purely rasterized opacity heuristic. Geometry Field Splatting defines a stochastic geometry field

$v(t)=0$9

where the kernels are Gaussian surfels lying on tangent planes. Instead of splatting volumetric density directly, the method splats the geometry field and derives a ray-dependent density through opaque-surface theory, including the factor

$\mathrm{opacity}_{color}$0

This yields a closed-form opacity footprint

$\mathrm{opacity}_{color}$1

and rendering with exact transmittance and self-attenuation, up to the practical approximation of global sorting (Jiang et al., 2024).

A third branch treats standard Gaussians themselves as stochastic solids. Geometry-Grounded Gaussian Splatting derives the vacancy field

$\mathrm{opacity}_{color}$2

for a Gaussian occupancy $\mathrm{opacity}_{color}$3, and then defines attenuation by

$\mathrm{opacity}_{color}$4

This replaces heuristic depth from alpha compositing with a volumetric transmittance model and median depth

$\mathrm{opacity}_{color}$5

which the method uses as a sharper and more view-consistent geometric signal than expected depth (Zhang et al., 25 Jan 2026).

A fourth branch decouples appearance and geometry without removing either. Geometry Gaussians adds a single scalar $\mathrm{opacity}_{color}$6 to each splat, alongside the usual $\mathrm{opacity}_{color}$7. RGB rendering uses only $\mathrm{opacity}_{color}$8, while depth and normals use only $\mathrm{opacity}_{color}$9. The method therefore argues that default 3DGS is “inheritedly unsuited to represent texture and geometry at the same time,” and that explicit opacity disentanglement removes this conflict (Zhou et al., 3 Jun 2026).

These formulations suggest that GeoGS is less a single primitive type than a spectrum of representational choices about where surface geometry should reside: in anisotropic covariances, in planar surfels, in a stochastic geometry field, in a stochastic-solid transmittance model, or in a geometry-specific opacity channel.

3. Geometry-centric supervision and optimization

The defining feature of GeoGS is not only representation but supervision. In 360-GeoGS, the central mechanism is Depth-Normal geometric regularization. The method flattens each Gaussian along its smallest scale by

$\mathrm{opacity}_{geo}$0

defines an intersection depth

$\mathrm{opacity}_{geo}$1

and recovers normals from depth gradients through a cross product. The resulting D-Normal loss enforces consistency between rendered normals and target normals, thereby directly supervising Gaussian position $\mathrm{opacity}_{geo}$2, rotation $\mathrm{opacity}_{geo}$3, and scale $\mathrm{opacity}_{geo}$4. The full objective combines photometric loss, scale flattening, depth loss, and D-Normal loss with hyperparameters $\mathrm{opacity}_{geo}$5, $\mathrm{opacity}_{geo}$6, and $\mathrm{opacity}_{geo}$7 (Yao et al., 5 Jan 2026).

GeoGaussian operationalizes geometry preservation through initialization and constrained densification. Smoothly connected points receive thin, normal-aligned ellipsoids; clones are displaced only in the tangent plane via

$\mathrm{opacity}_{geo}$8

and splits are constrained to remain co-planar. Optimization uses a geometric consistency loss combining plane-offset consistency and normal alignment, denoted $\mathrm{opacity}_{geo}$9, and the training schedule runs photometric-only for the first $59$0 iterations, with densification ending at $59$1 and full training at approximately $59$2 (Li et al., 2024).

GeoSplat extends geometry-only supervision from first-order to second-order structure. Its manifold- and varifold-based estimators refresh normals, tangent directions, principal curvatures, and principal directions during training. These priors shape initialization, truncation of position gradients in the normal direction, curvature-aligned covariance warm-up, and geometry-aware densification. The method adds two explicit regularizers,

$59$3

for curvature-consistent anisotropy and small normal scale, and

$59$4

for alignment of Gaussian axes with principal directions and normal, yielding

$59$5

It also upsamples flat regions using mean absolute curvature rather than mean curvature, specifically to avoid failure on surfaces such as helicoids whose mean curvature is zero but whose bending is not (Li et al., 5 Sep 2025).

Sparse2DGS shows a different route to geometry-first optimization under sparse views. It initializes from CLMVSNet depth, back-projects MVS points to Gaussian centers, samples appearance features $59$6 and colors $59$7 once, and then keeps both fixed throughout optimization. The key losses are feature splatting,

$59$8

Direct Gaussian Primitive Regularization, which reparameterizes a primitive as $59$9, normal alignment, and 2DGS depth-normal and depth-distortion terms. The full objective is

$10$0

with $10$1, $10$2, $10$3, and $10$4. Instead of standard densification, it uses Selective Gaussian Update every $10$5 steps, reprojecting rendered cues back to positions only when rendered NCC is superior to Gaussian-primitive NCC (Wu et al., 29 Apr 2025).

Geometry-Grounded Gaussian Splatting replaces heuristic depth with volumetric median depth and backpropagates gradients to all Gaussians along the ray through the implicit relation $10$6. Its loss combines RGB, depth-derived normal consistency, and multi-view regularization consisting of patch NCC and geometric cycle consistency:

$10$7

with $10$8, $10$9, $83.1\%$0, and $83.1\%$1 (Zhang et al., 25 Jan 2026).

Across these methods, a consistent pattern emerges: geometry-only or geometry-first Gaussian splatting is achieved either by suppressing appearance degrees of freedom, by separating appearance and geometry into different pathways, or by injecting explicit geometric structure into initialization, updates, and densification.

4. Specialized formulations: panoramas, dynamics, and SLAM

For panoramic reconstruction, 360-GeoGS adapts feed-forward 3DGS to equirectangular images. It uses a SphereCNN backbone to construct a spherical cost volume, predicts an initial dense depth prior, aggregates high-level features into $83.1\%$2, modulates low-level features through FiLM, and regresses per-pixel Gaussian parameters at full panorama resolution $83.1\%$3. Depth gradients and normals are computed directly in spherical image space, which the method uses to avoid seam artifacts and to handle strong projection distortions from 360 cameras. The intended setting is indoor panoramic reconstruction from one or more 360 panoramas with known camera-to-world poses (Yao et al., 5 Jan 2026).

For dynamic scenes, VeGaS makes GeoGS a mode of a broader 4DGS system. Standard 4DGS couples motion and geometry through a single 4D covariance, so updates to $83.1\%$4 affect both conditional mean and conditional covariance. VeGaS instead introduces a Galilean shearing matrix

$83.1\%$5

which changes the time-dependent mean trajectory while leaving the conditional spatial covariance invariant by Schur complement invariance. The GeoGS configuration is obtained by setting $83.1\%$6 and disabling the Geometric Deformation Network, so that $83.1\%$7 and the splats become time-invariant (Zhang et al., 1 Mar 2026).

For dense monocular SLAM, GeoGS-SLAM turns geometry-only Gaussian splatting into a complete system. It combines a DROID-SLAM front-end, monocular depth and normal priors from Omnidata, and a Gaussian back-end whose primitives have only center, rotation, planar scales, and opacity. The renderer predicts depth

$83.1\%$8

and normals

$83.1\%$9

with no color modeling. Training uses single-view geometric losses and multi-view photometric consistency induced by rendered depth. The system also introduces a coherent loop-closure update: after pose correction, revisited Gaussians are globally transformed by a single estimated Sim(3), rather than by inconsistent per-viewpoint corrections, to prevent map tearing (Zhou et al., 8 Jul 2026).

For appearance-geometry disentanglement in complex materials, Geometry Gaussians provides a distinct but closely related specialization. It adds only one scalar per primitive, $\mu \in \mathbb{R}^3$0, yet uses it to render an unbiased geometry depth $\mu \in \mathbb{R}^3$1 and geometry normals independently of the photometric depth $\mu \in \mathbb{R}^3$2. A discrepancy mask

$\mu \in \mathbb{R}^3$3

is then combined with transparent-region segmentation to drive detection-guided supervision and a transparency-aware masked MVS loss. This is particularly targeted at transparent and reflective scenes where default 3DGS cannot make one opacity parameter serve both appearance and geometry (Zhou et al., 3 Jun 2026).

These variants show that GeoGS is not tied to a single application domain. The same design principle—separating geometric reasoning from appearance overfitting—has been used for 360 imagery, sparse-view reconstruction, dynamic 4D scenes, transparent objects, and online monocular SLAM.

5. Empirical performance

Reported results span novel-view synthesis, depth estimation, surface reconstruction, and SLAM benchmarks. The numbers vary because the underlying problem settings differ substantially, but the central empirical claim is consistent: stronger geometric structuring improves depth, surface quality, or map quality without necessarily collapsing rendering performance.

Setting	Dataset	Reported result
360-GeoGS (Yao et al., 5 Jan 2026)	HM3D / Replica	Abs Diff $\mu \in \mathbb{R}^3$4; RMSE $\mu \in \mathbb{R}^3$5; PSNR $\mu \in \mathbb{R}^3$6; HM3D Chamfer $\mu \in \mathbb{R}^3$7
Geometry Field Splatting (Jiang et al., 2024)	DTU / BlendedMVS	DTU average Chamfer $\mu \in \mathbb{R}^3$8 with latent reflectance; BlendedMVS scene-level average $\mu \in \mathbb{R}^3$9 with SH
Sparse2DGS (Wu et al., 29 Apr 2025)	DTU 3-view	Mean Chamfer Distance $R \in SO(3)$0; training time $R \in SO(3)$1 min
Geometry Gaussians (Zhou et al., 3 Jun 2026)	TransLab / DTU	TransLab PSNR $R \in SO(3)$2, CD $R \in SO(3)$3, F1 $R \in SO(3)$4; DTU mean CD $R \in SO(3)$5
Geometry-Grounded GS (Zhang et al., 25 Jan 2026)	DTU / Tanks & Temples	DTU mean CD $R \in SO(3)$6–$R \in SO(3)$7 mm; Tanks & Temples mean F1 $R \in SO(3)$8
GeoGS-SLAM (Zhou et al., 8 Jul 2026)	Replica / ScanNet++ / DTU	Replica Avg Acc. $R \in SO(3)$9 cm, Comp. $\mathbf{s}=(s_1,s_2,s_3)^\top$0 cm, ATE $\mathbf{s}=(s_1,s_2,s_3)^\top$1 cm; ScanNet++ CD $\mathbf{s}=(s_1,s_2,s_3)^\top$2 cm; DTU CD $\mathbf{s}=(s_1,s_2,s_3)^\top$3 cm

Within the 360-imaging regime, 360-GeoGS reports depth gains over panoramic baselines: on HM3D, Abs Diff improves from $\mathbf{s}=(s_1,s_2,s_3)^\top$4 for Splatter-360 and $\mathbf{s}=(s_1,s_2,s_3)^\top$5 for MVSplat to $\mathbf{s}=(s_1,s_2,s_3)^\top$6, while 3D reconstruction improves from Splatter-360’s accuracy/completeness/Chamfer of $\mathbf{s}=(s_1,s_2,s_3)^\top$7 and MVSplat’s $\mathbf{s}=(s_1,s_2,s_3)^\top$8 to $\mathbf{s}=(s_1,s_2,s_3)^\top$9. Its ablation also shows that removing D-Normal regularization drops PSNR from $v(t)=0$00 to $v(t)=0$01 and increases Chamfer from $v(t)=0$02 to $v(t)=0$03, while removing both D-Normal and scale flattening further degrades PSNR to $v(t)=0$04 and Chamfer to $v(t)=0$05 (Yao et al., 5 Jan 2026).

For opaque-surface reconstruction, Geometry Field Splatting reports a DTU average Chamfer Distance of $v(t)=0$06 with latent reflectance and $v(t)=0$07 with SH, compared with $v(t)=0$08 for 2DGS and $v(t)=0$09 for RaDe-GS. On BlendedMVS, the SH variant reaches the best scene-level average of $v(t)=0$10 and the best object-centric average of $v(t)=0$11. Runtime is approximately $v(t)=0$12 minutes for the SH version and $v(t)=0$13 minutes for the latent version, compared with $v(t)=0$14 minutes for 2DGS and more than $v(t)=0$15 hours for Neuralangelo (Jiang et al., 2024).

For sparse-view surface reconstruction, Sparse2DGS reports a DTU three-view mean Chamfer Distance of $v(t)=0$16, outperforming 2DGS at $v(t)=0$17, GOF at $v(t)=0$18, and PGSR at $v(t)=0$19. It is reported as approximately $v(t)=0$20 faster than SparseNeus, with a training time of $v(t)=0$21 minutes versus $v(t)=0$22 minutes, and much faster than NeuSurf at $v(t)=0$23 hours (Wu et al., 29 Apr 2025).

For transparent scenes, Geometry Gaussians reports on TransLab: PSNR $v(t)=0$24, CD $v(t)=0$25, F1 $v(t)=0$26, and training time $v(t)=0$27h. On the same dataset, TSGS reports PSNR $v(t)=0$28, CD $v(t)=0$29, F1 $v(t)=0$30, and training time $v(t)=0$31h; PGSR reports PSNR $v(t)=0$32, CD $v(t)=0$33, and F1 $v(t)=0$34; 2DGS reports PSNR $v(t)=0$35, CD $v(t)=0$36, and F1 $v(t)=0$37. On NeRF Synthetic, the same method reports PSNR $v(t)=0$38, CD $v(t)=0$39, and F1 $v(t)=0$40, while on Mip-NeRF360 it reports overall PSNR $v(t)=0$41 and indoor PSNR $v(t)=0$42 (Zhou et al., 3 Jun 2026).

For geometry-grounded reconstruction, Geometry-Grounded Gaussian Splatting reports mean Chamfer Distance of $v(t)=0$43–$v(t)=0$44mm on DTU and mean F1-score $v(t)=0$45 on Tanks & Temples, with average optimization times of $v(t)=0$46–$v(t)=0$47 minutes and about $v(t)=0$48 minutes, respectively. The paper contrasts these results with PGSR at $v(t)=0$49mm on DTU and $v(t)=0$50 F1 on Tanks & Temples, GOF at $v(t)=0$51mm and $v(t)=0$52, and 2DGS at $v(t)=0$53mm and $v(t)=0$54 (Zhang et al., 25 Jan 2026).

For SLAM, GeoGS-SLAM reports on Replica an average accuracy of $v(t)=0$55cm, completeness $v(t)=0$56cm, completeness ratio $v(t)=0$57, and ATE $v(t)=0$58cm. On ScanNet++, it reports ATE $v(t)=0$59cm and CD $v(t)=0$60cm; on ScanNet, average ATE $v(t)=0$61cm; and on DTU, average CD $v(t)=0$62cm under a two-minute budget. The same paper emphasizes that GeoGS uses far fewer Gaussians and less storage than appearance-inclusive baselines: on DTU Scan55, $v(t)=0$63 Gaussians and $v(t)=0$64MB, compared with $v(t)=0$65 and $v(t)=0$66MB for 2DGS, $v(t)=0$67 and $v(t)=0$68MB for PGSR, and $v(t)=0$69 and $v(t)=0$70MB for QGS (Zhou et al., 8 Jul 2026).

6. Limitations, misconceptions, and likely directions

The limitations are highly formulation-dependent. 360-GeoGS assumes indoor scenes and accurate camera poses, and its geometry depends on a good spherical depth prior and consistent panoramic calibration; reflective or transparent surfaces and severe occlusions can still cause local misalignment (Yao et al., 5 Jan 2026). Geometry Field Splatting is designed for opaque solids and does not handle transparency, semi-transparent materials, participating media, or fuzzy objects well; its exactness also relies on either non-overlapping intersections or fully overlapped intersections with identical color, while practical efficiency uses global rather than per-ray sorting (Jiang et al., 2024). GeoGaussian is sensitive to normal and plane estimation, especially for distant geometry or cluttered scenes, and excessive geometric weights can flatten fine structure (Li et al., 2024). GeoSplat notes that curvature estimation can remain challenging near singularities and thin structures, and that bandwidth selection and neighborhood size are sensitive hyperparameters (Li et al., 5 Sep 2025). Sparse2DGS still depends on MVS quality, lacks explicit robust visibility weighting and silhouette constraints, and can fail when sparse-view MVS depth or features are unreliable (Wu et al., 29 Apr 2025). Geometry Gaussians depends on transparent-region segmentation, thresholding in $v(t)=0$71, and foundation-model supervision that may be noisy or non-metric (Zhou et al., 3 Jun 2026). Geometry-Grounded GS retains the independence assumption in $v(t)=0$72, requires bracketing for binary search, and still renders RGB and normals rasterically rather than volumetrically (Zhang et al., 25 Jan 2026). GeoGS-SLAM assumes static environments and does not target photorealistic novel-view synthesis (Zhou et al., 8 Jul 2026).

Several misconceptions recur across the literature. One is that geometry-only necessarily means colorless rendering. In fact, some works are strictly geometry-only, such as GeoGS-SLAM, while others merely prioritize or decouple geometry. Another is that geometry-only always implies lower rendering quality. 360-GeoGS explicitly reports competitive rendering quality while improving geometric consistency, and Geometry Gaussians argues that decoupling opacity can improve rendering and geometry simultaneously in transparent scenes (Yao et al., 5 Jan 2026, Zhou et al., 3 Jun 2026). A third is that better geometry must come from abandoning Gaussian splatting in favor of meshing or full volumetric rendering. The stochastic-solid and geometry-field papers instead show that the Gaussian representation itself can be reinterpreted in a more geometrically principled way, with exact or almost exact transmittance, closed-form footprints, or median-depth rendering, while remaining within a splatting-based framework (Zhang et al., 25 Jan 2026, Jiang et al., 2024).

The literature also outlines a clear forward path. 360-GeoGS identifies pose-free reconstruction from 360 images, generative filling for occluded regions, meshing from Gaussians using normals and intersection depths, multi-sensor fusion with IMU or LiDAR, and temporal consistency across panoramic sequences as plausible extensions (Yao et al., 5 Jan 2026). VeGaS suggests higher-order motion models and stronger geometric priors for difficult dynamic sequences (Zhang et al., 1 Mar 2026). GeoSplat points to improved handling of discontinuities and uncertainty-aware geometry scheduling (Li et al., 5 Sep 2025). Geometry Gaussians suggests that geometry-only outputs can be combined with existing geometry-aware surface extraction pipelines (Zhou et al., 3 Jun 2026). Taken together, these directions suggest that GeoGS is evolving from a narrow reconstruction trick into a broader design principle for Gaussian-based spatial representation: preserve the computational advantages of splatting, but make geometry a first-class, explicitly modeled quantity rather than a by-product of photometric optimization.