Occlusion-Aware 2D Gaussian Surfels

• The paper presents improved occlusion handling by replacing global depth sorting with per-ray ordering to eliminate popping and blending artifacts.
• It employs surface-aligned Gaussian surfels with explicit ray-surface intersections that provide accurate per-ray depth for enhanced hidden-surface consistency.
• The method integrates opaque and semi-opaque layers through depth peeling and visibility-conditioned accumulation to achieve robust hybrid compositing.

Searching arXiv for the core papers on 2D Gaussian surfels, visibility, and related hybrid renderers. Occlusion-aware 2D Gaussian surfels are surface-aligned Gaussian primitives rendered with visibility reasoning that goes beyond unconstrained, view-global Gaussian ordering. In the recent literature, the phrase does not denote a single canonical algorithm. Instead, it covers a family of methods that represent scenes with planar or tangent-plane Gaussian elements and then improve hidden-surface consistency through one or more of the following mechanisms: per-ray depth sorting, opaque or semi-opaque surfel layers with z-buffering or depth peeling, visibility-conditioned Gaussian accumulation, local-map isolation of visible surfaces, or ray-traced transmittance for secondary transport. Across these variants, the common motivation is that standard Gaussian splatting pipelines can produce popping artifacts, blended-depth errors, or occlusion leakage when visibility is approximated only from primitive-center depth or from globally shared per-view ordering (Song et al., 2024).

1. Surface-aligned Gaussian primitives

The core representational idea is to replace volumetric 3D Gaussian blobs with local surface elements. In the 2D Gaussian Splatting lineage, each primitive is a planar Gaussian surfel parameterized by a center $\mathbf{p}$, two principal tangential axes $\mathbf{t_u}, \mathbf{t_v}$, two scale factors $s_u, s_v$, opacity $\alpha$, and appearance parameters. The local surfel normal is given by

$$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$

with sign chosen toward the viewing direction, and the local tangent-plane mapping is

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$

Given a pixel ray, the ray-surfel intersection is computed explicitly through

$$\mathbf{x} = (xz, yz, z, z)^\top = \mathbf{P}\mathbf{H}(u, v, 1, 1)^\top,$$

and the local footprint is weighted by

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

This explicit ray-surface intersection is the geometric basis for many later visibility corrections, because it provides actual per-ray depth rather than only a center-depth proxy (Song et al., 2024).

Several subsequent systems preserve this planar formulation. Surgical Gaussian Surfels define a surface-aligned elliptical splat with local parameterization

$P(u, v) = p_k + s_u t_u u + s_v t_v v,$

and a local-to-world transform with zero third component,

$$H = \begin{bmatrix} s_u t_u & s_v t_v & 0 & p_k\ 0 & 0 & 0 & 1 \end{bmatrix},$$

together with the local 2D Gaussian

$\mathbf{t_u}, \mathbf{t_v}$0

ObjSplat similarly parameterizes Gaussian surfels with a rank-deficient covariance,

$\mathbf{t_u}, \mathbf{t_v}$1

so that each primitive is explicitly planar rather than volumetric (Sunmola et al., 6 Mar 2025, Li et al., 11 Jan 2026).

A related but distinct branch uses opaque surfels as the primary surface layer and Gaussian splats only as a secondary detail field. Gaussian-enhanced Surfels define the coarse geometry with 2D opaque surfels

$\mathbf{t_u}, \mathbf{t_v}$2

where each surfel is “a 2D unit circular disc on the XY-plane in its local coordinate,” transformed by anisotropic scaling, rotation, and translation. In the 2D-GES variant, the second-layer detail primitives are also 2D Gaussians rather than 3D Gaussians, bringing the architecture closer to a fully surface-based 2D surfel-plus-2D-Gaussian design (Ye et al., 24 Apr 2025).

This body of work indicates that “2D Gaussian surfel” is not merely shorthand for a flattened covariance. It is an explicit surface prior: local tangent geometry, intrinsic normals, and ray-surface intersection semantics.

2. Why visibility becomes a first-class problem

The need for occlusion-aware surfels arises because front-to-back alpha compositing is only as correct as the order in which primitives are blended. In standard Gaussian splatting rasterization, primitives are typically sorted once per view using primitive-center depth and then traversed by the same global order for all rays. HDGS identifies this as a source of popping artifacts, especially for large, thin, or oblique surfels whose depth varies significantly across their extent. Because 2DGS computes explicit ray-surfel intersections, the depth of the actual hit point can differ materially from the center depth, and a single global order can therefore be incorrect even within one image (Song et al., 2024).

This observation generalizes beyond novel-view rendering quality. GauS-SLAM argues that Gaussian-based tracking degrades because rendered geometry itself is inconsistent across viewpoints. It identifies two coupled causes: first, center-depth modeling of Gaussian primitives yields multi-view inconsistent depth estimations; second, even when a farther surface has small blending weight, its much larger depth can still corrupt the blended depth used for tracking. In its chair example, the floor behind a chair backrest contributes to the rendered depth, producing an ill-blended depth despite visually plausible color compositing (Su et al., 3 May 2025).

Several papers make the same distinction in different forms. In GES, the problem is not only sorting artifacts but also the leakage that occurs when all Gaussians are accumulated without a coarse visibility owner. In that framework, surfels establish the main visible surface, and only Gaussians whose center depth is in front of the surfel depth map are allowed to contribute. This avoids the color leakage associated with purely weighted-sum Gaussian rendering while also avoiding global Gaussian sorting (Ye et al., 24 Apr 2025). DP-GES sharpens this argument further: hard-opaque surfel boundaries cause aliasing, while purely sort-free Gaussian accumulation causes leakage or popping. The remedy is to recover per-pixel ordered surfel layers where ordering matters, rather than assuming a single opaque cut or a fully order-agnostic accumulation (Ye et al., 25 May 2026).

A different manifestation appears in active reconstruction. ObjSplat argues that opacity-only or simple depth-based visibility cues are insufficient because a region can be “covered” yet still be back-facing, self-occluded, or visible only from an invalid side. It therefore augments rendered depth and opacity with explicit back-face tests and occlusion-aware covisibility evaluation, using

$\mathbf{t_u}, \mathbf{t_v}$3

and

$\mathbf{t_u}, \mathbf{t_v}$4

Here visibility reasoning is used not to change the primary renderer, but to decide which surfels are actually well observed and which viewpoints are informative (Li et al., 11 Jan 2026).

These formulations suggest that “occlusion-awareness” in 2D Gaussian surfels is broader than hidden-surface removal in the strict rasterization sense. It includes correcting per-ray ordering, preventing hidden layers from contaminating depth, gating residual detail by a visible surface layer, and reasoning about covisibility or back-face validity in downstream reconstruction and planning.

3. Per-ray ordering and depth-corrected compositing

The most direct occlusion-aware strategy is to preserve alpha compositing but correct the ordering. HDGS is the clearest instance. It replaces global per-view primitive sorting with per-ray depth sorting. For each pixel ray and each intersected surfel, it computes the actual intersection depth $\mathbf{t_u}, \mathbf{t_v}$5 through the explicit 2DGS ray-surfel formulation, sorts intersected surfels by that depth, and composites them front-to-back. Its final rendering equation is

$\mathbf{t_u}, \mathbf{t_v}$6

where “the index $\mathbf{t_u}, \mathbf{t_v}$7 follows the k-sorted order,” and

$\mathbf{t_u}, \mathbf{t_v}$8

Implementation is approximate rather than exact: it uses per-ray k-buffer sorting and per-tile sorting, with tile size $\mathbf{t_u}, \mathbf{t_v}$9, and ray sort buffer size $s_u, s_v$0 for synthetic scenes and $s_u, s_v$1 for real scenes (Song et al., 2024).

The empirical visibility evidence is unusually explicit. HDGS adopts the sorting-error metric

$s_u, s_v$2

averaged over image rays, and reports: 2DGS train $s_u, s_v$3, test $s_u, s_v$4; HDGS w/o prune train $s_u, s_v$5, test $s_u, s_v$6; HDGS w/ prune train $s_u, s_v$7, test $s_u, s_v$8. In the NeRF synthetic ablation, removing ray sorting reduces performance from PSNR 33.46, SSIM 0.968, LPIPS 0.030 to PSNR 31.99, SSIM 0.955, LPIPS 0.048, and the paper states that ray sorting causes the most significant drop when removed (Song et al., 2024).

GauS-SLAM pursues a related but distinct correction: it accepts front-to-back alpha blending yet treats the blended depth itself as the visibility problem. After computing unbiased ray-surface intersection depths $s_u, s_v$9, it finds a median depth $\alpha$0 as the first surfel along the ray where cumulative opacity exceeds $\alpha$1, then adjusts behind-surface depths toward this dominant visible-surface depth: $\alpha$2 with

$\alpha$3

and final normalized depth

$\alpha$4

This is not hard visibility or per-ray surfel selection, but a soft occlusion-aware depth correction designed to suppress hidden-surface interference in tracking and mapping (Su et al., 3 May 2025).

Both methods remain alpha-composited surfel renderers. Neither introduces exact hidden-surface removal for opaque surfaces, and neither is order-independent transparency. Their contribution is more specific: visibility-corrected surface splatting through depth-accurate ray ordering or depth-aware suppression of hidden layers.

4. Surface-first visibility: opaque surfels, depth peeling, and hybrid layers

A second family of methods solves visibility by assigning the primary surface layer to explicit surfels and treating Gaussian detail as secondary. In GES, rendering is two-pass. First, opaque 2D surfels are rasterized through a standard graphics pipeline: “We compute the depths of surfel fragments, perform the depth test with a z-buffer, and write the colors of fragments passing the depth test.” This yields a surfel color map $\alpha$5 and depth map $\alpha$6. Second, Gaussians are splatted and accumulated only if their center depth passes the surfel depth test: $\alpha$7

$\alpha$8

and

$\alpha$9

The method is therefore sorting-free for the Gaussian enhancement pass because coarse visibility has already been externalized to the surfel z-buffer (Ye et al., 24 Apr 2025).

The same paper makes an important representational distinction. In final rendering, surfels are opaque discs, not Gaussian surfels. During training, however, a surfel is modulated by

$$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$0

so when $$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$1 the surfel behaves like a 2D Gaussian and gradually hardens into an opaque disk. This suggests a continuum between Gaussian-like soft surfels and hard surfel visibility within the same architecture (Ye et al., 24 Apr 2025).

DP-GES extends this hybrid logic by softening surfel boundaries and recovering multiple local layers with depth peeling. The surfel alpha profile is

$$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$2

with final $$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$3, producing “a large opaque center and a thin semi-transparent boundary.” The renderer peels the nearest three surfel layers per pixel,

$$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$4

and composites them front-to-back: $$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$5 Gaussians are still splatted sort-free, but each Gaussian is modulated by the peeled surfel transmittance interval

$$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$6

In this way, ordering is local and per-pixel where transparency matters, while the global Gaussian pass remains sorting-free (Ye et al., 25 May 2026).

The ablations show that three peeled layers are sufficient in practice: using two layers degrades quality significantly to $$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$7 PSNR versus $$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$8, while four layers provide negligible gain for much lower FPS. The same paper reports about 472 FPS at 1080p on an RTX 4090, compared with 675 FPS for GES and 185 FPS for vanilla 3DGS (Ye et al., 25 May 2026).

These hybrid systems are not “2D Gaussian surfels” in a uniform sense, because their primary surfels may be opaque discs rather than Gaussian-weighted translucent surfels. Yet they are central to the topic because they demonstrate an alternative interpretation of occlusion-awareness: surfels own visibility; Gaussian fields are residual appearance layers conditioned on that visibility.

5. Beyond primary visibility: covisibility, active perception, and ray-traced transport

A third strand moves occlusion-awareness out of the primary camera renderer and into higher-level geometry reasoning or physically based transport. ObjSplat is exemplary in the active reconstruction setting. Its Gaussian surfels are planar and depth-sorted for standard alpha compositing,

$$\mathbf{n} = \pm(\mathbf{t_u} \times \mathbf{t_v}),$$9

but the novel contribution is an explicit visibility analysis pipeline for planning. It computes back-face visibility from rendered normals, rendering-based cross-view covisibility, surfel-wise confidence, and uncertainty maps that combine opacity, back-face incompleteness, and observation history. In its ablation on viewpoint evaluation, opacity-only reaches PSNR 28.75, CD 0.701 mm, CR 86.02%, MC 3.84 m, whereas the full method reaches PSNR 32.35, CD 0.611 mm, CR 91.42%, MC 3.96 m; removing occlusion-awareness or back-face reasoning degrades completeness and geometry (Li et al., 11 Jan 2026).

At the physically based end of the spectrum, RadioGS and the adapted-radiosity framework turn Gaussian surfels into ray-queryable transport elements rather than only image-space splats. RadioGS represents each surfel with the 2DGS mapping

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$0

uses standard rasterized compositing for primary rendering,

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$1

but additionally defines a 2D Gaussian ray tracer

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$2

with

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$3

These are inserted into the physically based rendering equation

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$4

and the learned surfel radiance is regularized toward this physically rendered counterpart via the radiometric consistency residual

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$5

This is a markedly stronger notion of occlusion-awareness because visibility is queried for arbitrary incident directions rather than only along camera rays (Han et al., 2 Mar 2026).

An even broader transport formulation appears in “Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity,” which extends classic radiosity to semi-opaque 2D Gaussian surfels with continuous visibility. It defines each surfel by

$$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$6

and replaces binary visibility with transmittance products over surfel opacities. Its pairwise transport coefficient $$\mathbf{H} = \begin{bmatrix} s_u\mathbf{t_u} & s_v\mathbf{t_v} & 0 & \mathbf{p}\ 0 & 0 & 0 & 1 \end{bmatrix}.$$7 fuses cosine terms, inverse-square falloff, receiver weighting, sender opacity, and front-to-back transmittance, making visibility continuous and differentiable rather than hard and discontinuous (Jiang et al., 23 Sep 2025).

These works indicate that the phrase “occlusion-aware 2D Gaussian surfels” can also denote secondary visibility: shadowing, indirect illumination, covisibility, and back-face validity, not only frontmost-surface compositing.

6. Scope, limitations, and common interpretations

Across the literature, occlusion-aware 2D Gaussian surfels are best understood as a family of increasingly visibility-corrected surface-splatting methods rather than a single settled rendering theory. The most conservative members, such as HDGS, remain fundamentally alpha-composited surfel renderers with improved ordering. Their strengths are explicit ray-surfel intersection, per-ray depth extraction, and substantially reduced popping under viewpoint change; their limitations are that they still rely on alpha blending, approximate k-buffer/tile sorting, and do not perform exact hidden-surface removal (Song et al., 2024).

Hybrid methods such as GES and DP-GES shift the problem by assigning hard or semi-hard visibility to a surfel layer and using Gaussian splats as residual detail. This can be highly effective and sorting-free in the Gaussian pass, but it is not suited to true transparency, and its visibility semantics are anchored to opaque or near-opaque surface ownership rather than fully general multi-layer Gaussian compositing (Ye et al., 24 Apr 2025, Ye et al., 25 May 2026).

SLAM and reconstruction systems such as GauS-SLAM and ObjSplat show that occlusion-awareness is also a mapping issue. Hidden layers do not merely create visual artifacts; they bias rendered depth, corrupt tracking, and overestimate covisibility. Their solutions—surface-aware depth rendering, local visible-surface maps, back-face rejection, and occlusion-aware confidence—do not necessarily change the base compositing equation, but they do change which surfels are trusted, updated, or revisited (Su et al., 3 May 2025, Li et al., 11 Jan 2026).

Ray-traced inverse-rendering systems such as RadioGS and the adapted-radiosity method move closest to a full visibility model. They allow arbitrary-direction visibility queries, secondary-ray transport, and self-consistent indirect illumination over explicit 2D Gaussian surfels. Even there, however, visibility is still approximate: finite Monte Carlo sampling, soft transmittance rather than exact hard shadowing, and surfel-based transport approximations remain central (Han et al., 2 Mar 2026, Jiang et al., 23 Sep 2025).

A plausible synthesis is that the field has converged on three increasingly strong meanings of occlusion-awareness. The first is depth-order correctness, as in per-ray sorting and depth-adjusted blending. The second is surface-layer ownership, where surfels establish the visible manifold and Gaussian detail is gated by that manifold. The third is directional visibility reasoning, where surfels are queried by rays for covisibility, shadowing, or indirect transport. All three build on the same underlying representational shift: replacing volumetric Gaussian blobs with local planar Gaussian surface elements.