2D Gaussian Surfels Overview

• 2D Gaussian surfels are surface-aligned primitives defined by a 3D center, local tangent frames, and an intrinsic 2D Gaussian confined to a tangent plane.
• They are rendered by projecting each surfel into image space and computing exact ray–surfel intersections, ensuring view-consistent and geometrically faithful reconstructions.
• Their application in dynamic human modeling, inverse rendering, SLAM, and mesh extraction leverages explicit normals and local anisotropy, though sensitivity to initialization remains a challenge.

Searching arXiv for papers on 2D Gaussian surfels and 2D Gaussian Splatting. Searching for applications of 2D Gaussian surfels in dynamic humans, inverse rendering, SLAM, and mesh reconstruction. 2D Gaussian surfels are surface-aligned Gaussian primitives used to represent geometry and appearance as local planar patches embedded in 3D rather than as volumetric ellipsoids. Across recent Gaussian-splatting literature, they are described as small surface elements defined on tangent planes, endowed with explicit normals, anisotropic in-plane scale, opacity, and radiance or material attributes, then projected to image space and composited by alpha blending or related splatting rules. This representation is used for view-consistent surface modeling, dynamic human reconstruction, head avatars, inverse rendering, SLAM, road reconstruction, sparse-view reconstruction, text-to-3D generation, and mesh extraction (Tian et al., 29 Apr 2025, Su et al., 3 May 2025, Kouros et al., 25 Apr 2025, R. et al., 1 May 2026).

1. Definition and mathematical parameterization

A 2D Gaussian surfel is typically defined by a 3D center, a local tangent frame, and a 2D Gaussian distribution in local coordinates. In one common formulation, each surfel has center $\boldsymbol{p}_k \in \mathbb{R}^3$, tangent vectors $\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$, normal $$\boldsymbol{t}_w=\boldsymbol{t}_u \times \boldsymbol{t}_v$$, rotation matrix

$$\boldsymbol{R} = [\boldsymbol{t}_u,\boldsymbol{t}_v,\boldsymbol{t}_w],$$

and a scaling matrix whose normal-direction scale is zero, so that the primitive is disk-like rather than volumetric (Tian et al., 29 Apr 2025). The 3D embedding of local coordinates $(u,v)$ can be written as

$$\boldsymbol{P}(u,v)=\boldsymbol{p}_k+\boldsymbol{s}_u\boldsymbol{t}_u\,u+\boldsymbol{s}_v\boldsymbol{t}_v\,v,$$

while the intrinsic 2D Gaussian is

$$\mathcal{G}(u,v)=\exp\left(-\frac{u^2+v^2}{2}\right).$$

The associated 3D covariance retains the familiar decomposition

$$\boldsymbol{\Sigma}=\boldsymbol{R}\boldsymbol{S}\boldsymbol{S}^{\top}\boldsymbol{R}^{\top},$$

but the support is effectively two-dimensional because the third scale component is set to zero (Tian et al., 29 Apr 2025).

Equivalent parameterizations recur across the literature. Spec-Gloss Surfels defines each surfel by a center position $\mathbf{p}_k$, tangent directions $\mathbf{t}_u,\mathbf{t}_v$, explicit normal $\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$0, anisotropic in-plane scale $\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$1, and opacity $\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$2, then augments the primitive with material parameters such as diffuse albedo, specular reflectance, and roughness (Kouros et al., 2 Oct 2025). RGS-DR uses an analogous planar-disk model with center $\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$3, tangent frame, normal, opacity, and material attributes, again evaluating a 2D Gaussian in local UV coordinates after ray–plane intersection (Kouros et al., 25 Apr 2025).

Several works emphasize that the “2D” designation refers to the primitive’s support, not to the ambient space. The surfel lives at a 3D location and is oriented in 3D, but its Gaussian footprint is confined to a tangent plane. SurfSplat makes this explicit by writing the local scale as

$\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$4

and by deriving tangent vectors and normals from neighboring 3D positions before projecting the surfel to screen space (He et al., 2 Feb 2026). This suggests that the representation is best understood as a surface primitive with Gaussian weighting, rather than as a thin special case of a volumetric ellipsoid.

2. Projection, ray interaction, and compositing

Rendering with 2D Gaussian surfels proceeds by projecting each surface patch to image space and accumulating contributions along the viewing ray. In 2DGS-style rasterization, the projected footprint is a 2D Gaussian or filtered 2D Gaussian, and front-to-back alpha compositing takes the form

$\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$5

with splats depth-sorted along the ray (Kouros et al., 2 Oct 2025). The same compositing pattern is used not only for color but also for normals, roughness, depth, and other per-surfel attributes in deferred pipelines (Kouros et al., 25 Apr 2025).

A distinct geometric feature of 2DGS-family renderers is explicit ray–surfel interaction. HDGS states that, instead of projecting a volumetric Gaussian and approximating its covariance as in 3DGS, 2DGS computes the exact ray–surfel intersection to obtain local coordinates $\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$6 and depth $\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$7 for each surfel, then evaluates

$\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$8

Color, depth, and normal maps are then accumulated as

$\boldsymbol{t}_u,\boldsymbol{t}_v \in \mathbb{R}^3$9

with transmittance

$$\boldsymbol{t}_w=\boldsymbol{t}_u \times \boldsymbol{t}_v$$0

This exact intersection view of surfels underlies many claims about better geometric fidelity.

Deferred shading extends the primitive beyond radiance-only rendering. In RGS-DR and Spec-Gloss Surfels, surfels first rasterize a G-buffer of diffuse color, roughness, specular terms, normals, and auxiliary features; shading is then performed per pixel using explicit BRDF and environment lighting models rather than per-splat forward shading (Kouros et al., 25 Apr 2025, Kouros et al., 2 Oct 2025). RadioGS goes further by combining rasterization with 2D Gaussian ray tracing: surfels are intersected by secondary rays, alpha-blended along those rays, and used to define visibility and indirect radiance terms for inverse rendering (Han et al., 2 Mar 2026).

3. Relation to volumetric 3D Gaussians

The most consistent distinction in the literature is between volumetric 3D Gaussian ellipsoids and surface-constrained 2D Gaussian surfels. EfficientHuman states that 3D Gaussian methods for dynamic humans “struggle to effectively fit dynamic surface planes due to multi-view inconsistency and redundant Gaussians,” because “Gaussian ellipsoids cannot accurately represent the surfaces of dynamic objects,” whereas articulated 2D Gaussian surfels can conform to the moving body while ensuring view-consistent geometries (Tian et al., 29 Apr 2025). In the same spirit, GauS-SLAM attributes geometry distortion in Gaussian-based SLAM to the depth modeling of Gaussian primitives and the mutual interference between surfaces during depth blending; it replaces center-depth behavior with an unbiased intersection-depth model using 2D surfels (Su et al., 3 May 2025).

This contrast is especially pronounced for thin or explicit surfaces. SurfSplat argues that feedforward 3DGS methods often yield discrete, color-biased point clouds that may look plausible at normal resolution but reveal severe artifacts under close-up views, while 2DGS provides stronger anisotropy and higher geometric precision because the depth-axis scale is fixed to zero (He et al., 2 Feb 2026). Flash-Mono similarly motivates 2DGS by noting that volumetric 3D ellipsoids “often produce noisy geometry with ‘floater’ artifacts,” whereas planar 2D surfels provide stronger geometric priors and improved multi-view consistency in SLAM (Zhang et al., 3 Apr 2026).

The same argument appears in domain-specific settings. RoGs states that, because road surfaces have no thickness, a 2D Gaussian surfel is more consistent with the physical reality of the road surface than a 3D Gaussian sphere (Feng et al., 2024). MixedGaussianAvatar reports that pure 2D surfels reconstruct cleaner head geometry than 3DGS-based avatars, but also notes a trade-off: 2DGS improves geometric accuracy at the expense of rendering fidelity, motivating mixed 2D–3D representations in which surfels carry geometry and attached 3D Gaussians repair appearance where needed (Chen et al., 2024).

A plausible implication is that 2D Gaussian surfels function as a geometric prior first and a radiance primitive second. This is why they frequently appear in pipelines that care about normals, depth consistency, mesh extraction, or physically based shading, even when appearance modeling is later supplemented by volumetric or residual components.

4. Initialization, optimization, and deformation strategies

Although the primitive itself is simple, the literature places considerable emphasis on initialization and deformation. Sparse2DGS argues that, with only three input images, standard SfM yields poor initialization for Gaussian primitives, so it initializes 2D surfels from a dense point cloud formed by DUSt3R and COLMAP MVS, then optimizes color, depth distortion, and normal consistency without Gaussian densification (Takama et al., 26 May 2025). 2D-SuGaR likewise identifies sensitivity to initialization as a core weakness of 2DGS and introduces depth-guided initialization from monocular depth and normal priors, followed by DBSCAN-based pruning of degenerate Gaussians (R. et al., 1 May 2026).

Dynamic scenes introduce additional structure. EfficientHuman encodes surfels in canonical space and articulates them by Linear Blend Skinning driven by SMPL. It supplements this with a pose calibration module and an LBS optimization module, both introduced to correct misalignment and improve dynamic fitting (Tian et al., 29 Apr 2025). SurFhead makes a different deformation choice for head avatars: it binds 2D Gaussian surfels to FLAME triangles and replaces similarity transformations with affine Jacobian deformation, including inverse-transpose normal transformation and Jacobian Blend Skinning based on polar decomposition, to capture stretch and shear under extreme expressions (Lee et al., 2024).

Other works add geometry-specific regularization to compensate for sparse or ambiguous views. DirectGaussian introduces curvature-based cross-view normal consistency and a surface convergence loss for text-to-3D generation with four views (Dong et al., 8 Oct 2025). “Introducing Unbiased Depth into 2D Gaussian Splatting for High-accuracy Surface Reconstruction” replaces the original depth distortion loss with a depth convergence loss and changes the depth criterion used to determine the actual surface, specifically to address holes on glossy surfaces caused by reflection discontinuity and depth bias (Peng et al., 9 Mar 2025). SurfSplat enforces a surface continuity prior structurally by deriving rotations and scales from local geometry, and adds forced alpha blending to prevent opacity collapse in feedforward reconstruction (He et al., 2 Feb 2026).

These optimization choices indicate that 2D Gaussian surfels are rarely used as unconstrained primitives. They are usually tied to depth priors, normals, skeletons, meshes, or geometric consistency losses, reflecting a broader tendency to treat them as explicitly geometric carriers.

5. Major application domains

The representation has spread quickly because the same planar primitive supports very different tasks once coupled with domain-specific priors and losses.

Domain	Characteristic use of surfels	Representative papers
Dynamic humans and avatars	Surface-aligned body or head primitives, often articulated by SMPL or FLAME	(Tian et al., 29 Apr 2025, Chen et al., 2024, Lee et al., 2024)
Inverse rendering and relighting	Explicit normals, material attributes, deferred shading, ray tracing	(Kouros et al., 25 Apr 2025, Kouros et al., 2 Oct 2025, Han et al., 2 Mar 2026)
SLAM and real-time mapping	Surface-consistent depth, local maps, feed-forward or fused surfel states	(Su et al., 3 May 2025, Zhang et al., 3 Apr 2026, Pan et al., 1 Dec 2025)
Sparse-view and mesh reconstruction	Dense surface initialization, TSDF fusion, mesh extraction	(Takama et al., 26 May 2025, R. et al., 1 May 2026)
Text-to-3D and road surfaces	Surface generation under multi-view priors or structured scene constraints	(Dong et al., 8 Oct 2025, Feng et al., 2024)

In articulated human reconstruction, surfels are used to remain attached to moving surfaces through LBS or rig-based deformation, enabling dynamic view-consistent geometry (Tian et al., 29 Apr 2025). In head avatars, they are used because they provide fixed ray intersections and well-defined normals, which are useful for relighting, normal supervision, and mesh reconstruction (Lee et al., 2024).

In inverse rendering, the value of surfels is their explicit geometry. RGS-DR and Spec-Gloss Surfels both attach material parameters to surfels and render them through deferred shading, while RadioGS combines surfels with 2D Gaussian ray tracing and radiometric consistency so that learned radiance matches physically based rendering even for unobserved directions (Kouros et al., 25 Apr 2025, Kouros et al., 2 Oct 2025, Han et al., 2 Mar 2026).

In SLAM and online mapping, surfels are used as dense but surface-aware map primitives. GauS-SLAM builds an incremental RGB-D system around 2D Gaussian surfels and a Surface-aware Depth Rendering mechanism (Su et al., 3 May 2025). Flash-Mono uses a feed-forward frontend to predict per-pixel surfel attributes and a 2DGS backend for mapping (Zhang et al., 3 Apr 2026). EGG-Fusion combines geometry-aware Gaussian surfels with an information-filter-based fusion strategy to model multi-view consistent surfaces while maintaining real-time processing at 24 FPS and reporting a surface reconstruction error of 0.6 cm on Replica and ScanNet++ (Pan et al., 1 Dec 2025).

In sparse-view reconstruction and mesh extraction, surfels offer a practical compromise between explicit geometry and differentiable rendering. Sparse2DGS demonstrates accurate DTU reconstruction from only three images through dense point-cloud initialization (Takama et al., 26 May 2025), while 2D-SuGaR uses surfels as an intermediate surface-aware representation, then refines an extracted mesh with relaxed thin 3D Gaussians to achieve state-of-the-art DTU mesh reconstruction (R. et al., 1 May 2026).

6. Limitations, controversies, and current directions

Despite their geometric advantages, 2D Gaussian surfels are not free of failure modes. Several papers identify sensitivity to initialization as a major issue. 2D-SuGaR explicitly frames reliance on SfM as a weakness of 2DGS and uses monocular priors plus clustering-based pruning to stabilize training (R. et al., 1 May 2026). Sparse2DGS reaches a similar conclusion in sparse-view settings, arguing that dense and accurate point-cloud initialization is critical when only three views are available (Takama et al., 26 May 2025).

Glossy and view-dependent appearance remain difficult. The unbiased-depth paper reports that original 2DGS develops visible holes on glossy surfaces because reflection discontinuity introduces depth bias: high-opacity surfels drift behind the true surface, and the extracted surface depth becomes biased toward this false layer (Peng et al., 9 Mar 2025). ObjSplat notes that its current radiance model still struggles with high specularities, transparency, and extreme lighting variation (Li et al., 11 Jan 2026). In response, several inverse-rendering systems use surfels not as a complete solution but as a better geometric substrate for deferred BRDF evaluation, multi-level cube mipmaps, residual passes, or radiometric consistency constraints (Kouros et al., 25 Apr 2025, Kouros et al., 2 Oct 2025, Han et al., 2 Mar 2026).

Another recurring issue is the geometry–appearance trade-off. MixedGaussianAvatar reports that pure 2DGS produces excellent surface geometry but poorer rendering metrics than 3DGS-based baselines, which motivates mixed 2D–3D Gaussian trees in which surfels remain the primary carriers of geometry and 3D Gaussians repair difficult appearance regions (Chen et al., 2024). “When Gaussian Meets Surfel” adopts a related bi-scale view: opaque surfels represent coarse geometry and appearance, while a small number of Gaussians add fine-scale detail, with a 2D-GES variant replacing 3D Gaussians by 2D Gaussians for better geometry (Ye et al., 24 Apr 2025).

For SLAM and large-scale mapping, robustness to real capture remains open. GauS-SLAM notes sensitivity to motion blur and exposure changes, which can break multi-view consistency and introduce noisy surfaces (Su et al., 3 May 2025). RoGs highlights dependence on accurate vehicle poses for road-centric initialization (Feng et al., 2024). These observations suggest that, although 2D Gaussian surfels are often described as a geometrically faithful alternative to volumetric Gaussians, they still depend heavily on accurate priors, stable camera calibration, and appropriate regularization.

The current trajectory of the field points toward hybridization rather than exclusivity. Surfels are increasingly combined with articulated models, mesh priors, monocular geometric priors, point-cloud initializers, deferred shading, ray tracing, local-map SLAM backends, and mixed 2D–3D Gaussian schemes. This suggests that 2D Gaussian surfels are becoming a standard surface-centric primitive within a broader Gaussian graphics toolkit, especially where explicit normals, thin surfaces, mesh reconstruction, or physically based rendering are required.