Gaussian Surfels: Surface-Aligned 2D Gaussians

• Gaussian surfels are explicit 2D Gaussian primitives defined on local tangent planes with zero thickness along the normal direction.
• They are parameterized using anisotropic scales, rotations, and explicit normals to enable precise surface reconstruction and differentiable optimization.
• They are applied in hybrid radiance fields, SLAM, inverse rendering, and dynamic reconstruction to achieve high-fidelity visual and geometry outcomes.

Gaussian surfels are explicit surface-oriented Gaussian primitives that combine the optimization and rasterization advantages of Gaussian splatting with the surface alignment of surfels. In the literature, they are variously formulated as flattened 3D Gaussians whose local $z$-scale is set to $0$, as 2D Gaussians defined on a local tangent plane in 3D world space, or as planar anisotropic Gaussian kernels attached to local surface frames (Dai et al., 2024, Wang et al., 5 Apr 2025, Jiang et al., 2024). Across these formulations, the representation is used for high-quality surface reconstruction, radiance-field rendering, dynamic reconstruction, SLAM, inverse rendering, relighting, and active view planning, with later work extending it to hybrid surfel-Gaussian radiance fields, differentiable light transport, and geometry-aware online mapping (Ye et al., 24 Apr 2025, Su et al., 3 May 2025, Han et al., 2 Mar 2026).

1. Primitive definition and geometric parameterization

A common formulation treats a Gaussian surfel as a 3D Gaussian whose covariance is constrained to have zero thickness along one local axis. In "High-quality Surface Reconstruction using Gaussian Surfels" (Dai et al., 2024), the covariance is written as

$$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$

so the original 3D ellipsoid is collapsed into a 2D ellipse. The same paper identifies the local $z$-axis as the normal direction,

$\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$

which gives the optimizer an explicit tangent-normal decomposition rather than an unconstrained volumetric covariance.

An equivalent tangent-plane formulation appears in dynamic and generative work. "Video4DGen" defines a Gaussian surfel as a 2D Gaussian on a local tangent plane in 3D world space, parameterized by a center point $p_k^* \in \mathbb{R}^3$, tangent frame $(t_u^*, t_v^*)$, anisotropic in-plane scales $s_u^*, s_v^*$, rotation $\mathbf{R}_k^* \in \mathrm{SO}(3)$, and scaling matrix $\mathbf{S}_k^* = \mathrm{diag}(s_u^*, s_v^*, 0)$, with embedded point

$0$0

(Wang et al., 5 Apr 2025). "DirectGaussian" uses the same local-surface view, defining a surfel $0$1 by

$0$2

with learnable parameters $0$3 (Dong et al., 8 Oct 2025).

Sparse-view and generalizable systems adopt similar parameterizations but emphasize reduced degrees of freedom. "SmileSplat" represents each Gaussian surfel by 12 values,

$0$4

with covariance

$0$5

so the primitive has two in-plane scales and zero thickness along the normal direction (Li et al., 2024). "ObjSplat" uses

$0$6

again enforcing a locally planar, surface-aligned primitive (&&&10&&&).

This consistency of parameterization across otherwise different tasks suggests that the defining property of a Gaussian surfel is not a single rendering pipeline but a shared geometric prior: a Gaussian support restricted to a local tangent plane, with explicit orientation and in-plane anisotropy.

2. Rendering models, visibility, and optimization

Most Gaussian-surfel methods retain the splatting-style image formation of Gaussian rendering, but apply it to surface-aligned primitives. A representative form appears in "Video4DGen",

$0$7

with $0$8 (Wang et al., 5 Apr 2025). "RoGS" uses the same front-to-back alpha compositing form for road surfels after projection to 2D ellipses,

$0$9

and renders semantic vectors by replacing $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$0 with semantic labels (Feng et al., 2024). "SmileSplat" likewise renders color and depth by alpha compositing projected surfels, and optimizes camera intrinsics, extrinsics, and surfels jointly through differentiable rendering (Li et al., 2024).

A recurrent technical issue is that flattening the primitive improves geometric alignment but weakens or removes certain gradients. The 2024 reconstruction paper explicitly notes that when the $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$1-scale is set to $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$2, the derivatives to the local $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$3-axis computed from the covariance matrix are zero, so photometric loss alone cannot directly update the normal direction. Its remedy is a self-supervised normal-depth consistency loss,

$$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$4

together with monocular normal priors and foreground masks (Dai et al., 2024). That paper also introduces volumetric cutting over a $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$5 voxel grid to remove erroneous depth points caused by alpha blending, followed by screened Poisson reconstruction with tree depth 10.

Other work reformulates rendering more radically to improve surface fidelity. "Geometry Field Splatting with Gaussian Surfels" does not splat a density field directly; it splats a stochastic geometry field $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$6, derives an exact footprint

$$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$7

removes both the Taylor-series expansion of transmittance and the “no self-attenuation” assumption, and uses a color blending construction that guarantees the rendered color is a continuous function of the colors of the kernels, irrespective of ordering (Jiang et al., 2024). This paper is particularly important because it treats clustered surfels as the correct opaque-surface regime rather than as a failure case of volume splatting.

Optimization objectives are correspondingly geometry-aware. Depending on the application, papers combine photometric losses with depth distortion, normal consistency, opacity or mask losses, scale regularization, and geometric alignment terms. This shared loss structure reflects a central property of Gaussian surfels: they are not only rendering primitives but explicit local surface elements whose positions, normals, and support can be supervised directly.

3. Hybrid radiance fields, sorting-free rendering, and feed-forward prediction

A major branch of the literature uses Gaussian surfels as the coarse geometric scaffold of a hybrid radiance field. "When Gaussian Meets Surfel" introduces Gaussian-enhanced Surfels (GESs), a bi-scale representation in which a set of 2D opaque surfels with view-dependent colors represents coarse-scale geometry and appearance, and a few 3D Gaussians surrounding the surfels supplement fine-scale appearance details (Ye et al., 24 Apr 2025). Rendering is performed in two passes: surfels are first rasterized through a standard graphics pipeline to produce depth and color maps, and then Gaussians are splatted with depth testing and color accumulation on each pixel order independently. The result is entirely sorting-free rendering, which the paper associates with very fast rates, view-consistent images, and the avoidance of popping artifacts. The same work also defines Mip-GES, Speedy-GES, Compact-GES, and 2D-GES as anti-aliasing, speed, storage, and geometry-oriented extensions.

"Depth Peeling for High-Fidelity Gaussian-Enhanced Surfel Rendering" identifies a limitation of GES: the hard depth test on opaque surfels causes residual aliasing at object boundaries, because the surfel alpha is effectively clamped abruptly from $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$8 to $$\mathbf{\Sigma }_i = \mathbf{R}(\mathbf{r}_i)\, \mathrm{Diag}\left[ \left( \mathbf{s}_{i}^{x} \right) ^2, \left( \mathbf{s}_{i}^{y} \right) ^2, 0 \right] \mathbf{R}(\mathbf{r}_i)^{\top},$$9 once Gaussians are composited against it (Ye et al., 25 May 2026). Its solution, DP-GES, augments opaque surfels with semi-transparent boundaries using

$z$0

with $z$1, and introduces Depth Peeling to establish accurate per-pixel ordering. The final method peels three surfel layers per pixel, reuses peeled transmittance to modulate Gaussian splatting, remains sort-free in the Gaussian pass, and is described as eliminating aliasing and popping artifacts while enabling a fully differentiable joint optimization (Ye et al., 25 May 2026).

A separate line of work aims at generalizable or feed-forward Gaussian-surfel prediction. "SurfelSplat" generates pixel-aligned Gaussian surfel representations from sparse-view images, but argues that conventional feed-forward structures struggle because the spatial frequency of pixel-aligned primitives exceeds Nyquist sampling rates (Dai et al., 9 Apr 2026). It therefore introduces a cross-view feature aggregation module based on the Nyquist sampling theorem, first adapting the geometric forms of Gaussian surfels with spatial sampling rate-guided low-pass filters and then projecting the filtered surfels across all input views to obtain cross-view feature correlations. The paper reports that the model predicts Gaussian surfels within 1 second and offers a 100x speedup without costly per-scene training (Dai et al., 9 Apr 2026). "SmileSplat" addresses the related sparse, unposed-image setting with a multi-head Gaussian regression decoder, DSINE-based normal priors, and a Bundle-Adjusting Gaussian Splatting module that jointly optimizes Gaussian surfels and camera parameters (Li et al., 2024).

Text-conditioned generation extends the same representation into 3D content synthesis. "DirectGaussian" defines a text-to-3D surface generation pipeline that starts from text, uses conditional diffusion models to generate multi-view normal maps and texture images, predicts a coarse set of Gaussian surfel parameters, refines the surfels by differentiable 2D Gaussian splatting, and adds surface convergence and curvature consistency constraints to improve geometric coherence across views (Dong et al., 8 Oct 2025). In this setting, Gaussian surfels function as a surface-native alternative to meshes, voxel grids, and volumetric radiance fields.

4. Dynamic scenes, deformable objects, and avatars

Dynamic reconstruction methods use Gaussian surfels precisely because they are more geometry-aware than generic 3D Gaussians while remaining explicit and differentiable. "Adaptive and Temporally Consistent Gaussian Surfels for Multi-view Dynamic Reconstruction" reconstructs one frame at a time through per-frame incremental optimization, initializing each new frame from the previous one, applying a Neural Transformation Cache for coarse $z$2 alignment, and then refining center, rotation, scale, view-dependent color, and opacity in a fine stage (Chen et al., 2024). Its key technical additions are a unified adaptive gradient-aware densification strategy and a temporal consistency loss on curvature maps,

$z$3

to reduce temporal jittering. The same paper states that storage scales linearly with sequence length because each frame’s Gaussian representation is stored separately (Chen et al., 2024).

"Video4DGen" moves to a canonical-static plus continuous-warping formulation. Its Dynamic Gaussian Surfels (DGS) transform static surfels $z$4 into frame-dependent surfels $z$5 using sparse bones and dual quaternion blend skinning, with a continuous field $z$6 learned by an MLP (Wang et al., 5 Apr 2025). The paper adds warped-state geometric regularization so that the normal of the warped surfel aligns with the estimated surface normal in the warped state, and introduces a dual-branch refinement with $z$7 and $z$8 to preserve fine appearance details and reduce flickering and float-occlusion (Wang et al., 5 Apr 2025). In this framework, Gaussian surfels become deformable 4D primitives rather than static surface samples.

Avatar and surgical settings further emphasize deformation fidelity. "SurFhead" replaces similarity-style Gaussian-avatar deformation with 2D Gaussian surfels driven by affine deformation transfer from a face mesh, uses Jacobian Blend Skinning based on polar decomposition,

$z$9

and transforms normals with the inverse transpose,

$\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$0

to preserve geometric accuracy under stretch and shear (Lee et al., 2024). "Surgical Gaussian Surfels" constrains anisotropic point primitives into surface-aligned elliptical splats by constraining the scale component of the Gaussian covariance matrix along the view-aligned axis, predicts surfel motion fields with a lightweight MLP and locality constraints, and defines surface normals as

$\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$1

without requiring monocular normal priors (Sunmola et al., 6 Mar 2025).

Taken together, these works suggest that Gaussian surfels are especially useful when dynamic geometry is central: they provide fixed ray-surface intersections, explicit normals, and anisotropic support, while remaining compatible with differentiable optimization and densification.

5. SLAM, online mapping, and active reconstruction

In online reconstruction and SLAM, Gaussian surfels are adopted as a compromise between explicit surfel maps and differentiable Gaussian rendering. "GauS-SLAM" represents the scene with 2D Gaussian surfels attached to tangent planes and argues that 3D Gaussian primitives suffer from geometry distortion under novel viewpoints because the common center depth model leads to multi-view inconsistency (Su et al., 3 May 2025). To address this, it proposes a 2D Gaussian-based incremental reconstruction strategy, a Surface-aware Depth Rendering mechanism using unbiased intersection depth and depth adjustment,

$\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$2

and a local-map design that periodically isolates visible surfaces during tracking (Su et al., 3 May 2025). The paper reports state-of-the-art tracking on Replica and ScanNet++, with Replica ATE-RMSE of 0.06 cm and PSNR of 40.25 dB on Replica (Su et al., 3 May 2025).

"EGG-Fusion" frames Gaussian surfels as the central state variable of a real-time RGB-D reconstruction system (Pan et al., 1 Dec 2025). Each surfel is represented as

$\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$3

and repeated observations are fused with an information-form update,

$\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$4

over positions and normals (Pan et al., 1 Dec 2025). The paper states that the proposed system achieves a surface reconstruction error of 0.6 cm on Replica and ScanNet++, represents over 20\% improvement in accuracy compared to state-of-the-art GS-based methods, and maintains real-time processing at 24 FPS (Pan et al., 1 Dec 2025).

Active reconstruction pushes the representation beyond passive mapping. "ObjSplat" uses Gaussian surfels as a unified representation for reconstruction, rendering, view evaluation, and planning, with geometry-aware viewpoint evaluation that combines surfel-wise confidence, back-face observation, and visibility,

$\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$5

together with occlusion-aware multiview covisibility and next-best-path planning over a dynamically constructed spatial graph (Li et al., 11 Jan 2026). The paper reports that Ours-NBP achieves PSNR $\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$6, SSIM $\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$7, LPIPS $\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$8, CD $\mathbf{n}_i = \mathbf{R}(\mathbf{r}_i)[:,2],$9 mm, F-Score $p_k^* \in \mathbb{R}^3$0, CR $p_k^* \in \mathbb{R}^3$1, movement cost $p_k^* \in \mathbb{R}^3$2 m, and online time $p_k^* \in \mathbb{R}^3$3 s at convergence with 30 views (Li et al., 11 Jan 2026).

Domain-specific reconstruction further illustrates the flexibility of the primitive. "RoGS" models the road surface by placing Gaussian surfels at the vertices of a uniformly distributed square mesh, with each surfel storing color, semantic, and geometric information,

$p_k^* \in \mathbb{R}^3$4

and initializes height and rotation from vehicle trajectory geometry (Feng et al., 2024). Here the choice of a 2D Gaussian surfel is justified by the claim that the road surface has no thickness and that a 2D Gaussian surfel is more consistent with the physical reality of the road surface than a 3D Gaussian sphere (Feng et al., 2024).

6. Inverse rendering, relighting, and unresolved issues

For reflective and glossy appearance, Gaussian surfels are valued because they expose explicit normals and material parameters. "RGS-DR" uses a 2D Gaussian surfel representation for glossy and reflective objects, rasterizes geometric and material primitives into a deferred G-buffer storing diffuse color, roughness, specular tint, normals, features, and accumulated alpha, and computes shading with a multi-level cube mipmap and a residual pass with spherical-mipmap-based directional encoding (Kouros et al., 25 Apr 2025). Its image decomposition is written as

$p_k^* \in \mathbb{R}^3$5

which makes relighting and editing possible because geometry, materials, and lighting are explicitly separated (Kouros et al., 25 Apr 2025).

"Radiometrically Consistent Gaussian Surfels" introduces radiometric consistency as supervision for unobserved directions by minimizing the residual between each Gaussian primitive’s learned radiance and its physically based rendered counterpart,

$p_k^* \in \mathbb{R}^3$6

The paper combines Gaussian surfels with 2D Gaussian ray tracing and reports a finetuning-based relighting strategy with low rendering cost $p_k^* \in \mathbb{R}^3$7 ms and around 5.9 ms per frame for the finetuned surfel rendering path (Han et al., 2 Mar 2026).

"GOGS" similarly adopts a two-stage inverse-rendering pipeline: Stage I performs geometry reconstruction with a physics-based deferred rendering setup and split-sum approximation, enhanced by foundation-model depth and normal priors, while Stage II freezes geometry and optimizes material decomposition and lighting with Monte Carlo importance sampling of the full rendering equation and differentiable 2D Gaussian ray tracing (Yang et al., 20 Aug 2025). The paper reports average relighting PSNR of 24.89 on Glossy Synthetic, above GShader, Ref-GS, and IRGS (Yang et al., 20 Aug 2025).

The most explicit transport formulation appears in "Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity", which interprets Gaussian surfels as finite elements in a radiosity-style system with non-binary visibility and semi-opaque primitives (Jiang et al., 23 Sep 2025). It represents outgoing radiance and emission in spherical harmonics, solves transport with progressive refinement, Monte Carlo, and hybrid solvers, and derives an analytic backward pass that the paper states is about $p_k^* \in \mathbb{R}^3$8 faster than PyTorch autodiff (Jiang et al., 23 Sep 2025). This work makes clear that Gaussian surfels can be more than a surface proxy for rasterization; they can serve as the discrete support of explicit global illumination.

Several recurring limitations temper the representation’s scope. SurfelSplat identifies Nyquist-related failure modes in feed-forward sparse-view prediction when pixel-aligned primitives are too high-frequency for the available sampling rate (Dai et al., 9 Apr 2026). AT-GS states that memory and storage scale with sequence length because each frame representation is stored separately (Chen et al., 2024). RoGS highlights dependence on trajectory accuracy and sparse road texture (Feng et al., 2024). GOGS notes difficulty with mixed-material surfaces, increased computational cost from differentiable ray tracing and spherical encoding, and incomplete high-fidelity multi-bounce specular inter-reflections (Yang et al., 20 Aug 2025). These limitations indicate that Gaussian surfels are not a single settled design, but a family of surface-aligned Gaussian representations whose practical behavior depends strongly on how visibility, ordering, deformation, and light transport are modeled.

A common misconception is that Gaussian surfels are merely “3D Gaussian Splatting with one axis set to zero.” The literature is broader. Some methods do exactly flatten 3D Gaussians (Dai et al., 2024), some reinterpret surfels as kernels of a geometry field (Jiang et al., 2024), some use them as opaque or semi-transparent visibility scaffolds for auxiliary Gaussians (Ye et al., 24 Apr 2025, Ye et al., 25 May 2026), and others integrate them with continuous warping, information filtering, deferred shading, or radiosity (Wang et al., 5 Apr 2025, Pan et al., 1 Dec 2025, Jiang et al., 23 Sep 2025). What unifies these approaches is the insistence that explicit local surface structure—center, tangent plane, anisotropic support, and normal—should be preserved inside the Gaussian primitive itself.