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From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians

Conference: ECCV2026
Paper: ECCV Official
Area: 3D Vision
Keywords: Gaussian Splatting, surface reconstruction, oriented Gaussians, watertight meshes, occupancy field

TL;DR

The paper attaches a learnable oriented normal to every 3D Gaussian, reinterpreting it from an orientation-free symmetric blob into a stochastic surface element that attenuates only in its outward half-space; this restores the reciprocal attenuation assumed by Objects as Volumes-so occupancy and normal fields follow in closed form-and combined with a normal alignment loss, normal-aware densification and Primal Adaptive Meshing it sets a new state of the art on DTU and Tanks and Temples with only two pivots per Gaussian, far lighter meshes than concurrent work, and stable recovery of thin structures such as bicycle spokes.

Background & Motivation

Reconstructing high-quality 3D surfaces from a set of 2D images is a classic inverse problem in computer vision. Recent neural rendering-NeRF and 3D Gaussian Splatting (3DGS)-has pushed novel view synthesis to photographic quality, yet turning those renderings into explicit geometry remains hard because the two goals pull in opposite directions: neural rendering is built for soft, semi-transparent volumes, whereas surface reconstruction needs hard boundaries, and only hard boundaries can be turned into watertight geometry. Existing routes each have a weak spot. Implicit representations (SDF or occupancy fields such as NeuS, VolSDF and Neuralangelo) give continuous, topologically consistent surfaces but are extremely expensive to train, and their global solvers struggle with high-frequency detail, producing over-smoothed results. Explicit particle-based methods (3DGS itself) render in real time with high fidelity, but their primitives are unordered discrete particles, and there is no straightforward way to recover an ordered structure, i.e. a mesh, from them. Hybrid approaches in between (SuGaR, GOF, 2DGS, RaDe-GS, PGSR, VCR-GauS) regularize Gaussians toward the surface, but their extraction stage typically falls back on heuristics-typically TSDF fusion of blended depth maps plus a density threshold.

The deeper problem lies in how the primitive itself is interpreted. Standard practice treats a Gaussian as a symmetric blob of mass or density, whereas an orientable surface is inherently asymmetric: it is a boundary with empty space on one side and occupied space on the other. Modelling surface points with symmetric primitives implicitly assigns the same occupancy probability to both sides of a location, biasing the reconstruction. In standard 3DGS this bias is compounded by two technical obstacles. First, the 3DGS image formation model is not attenuation-based: a pixel's colour depends only on the value each Gaussian projects onto that pixel, not on how far the ray travels through the primitive, so Gaussian opacities are bounded in \([0,1]\) and cannot be identified with the unbounded attenuation coefficient \(\sigma\). The closed-form "occupancy ↔ attenuation" relation of Objects as Volumes-the theoretical backbone of NeuS-style methods-thus does not apply directly. Second, a flat Gaussian only defines a normal axis with no direction sign; once several Gaussians overlap with inconsistent orientations, blended depth maps provide neither consistent depth nor a reliable normal, and extraction degrades to TSDF-style heuristics. (The "blob" in the title refers to these orientation-free symmetric Gaussians; "spokes" refers both to the bicycle-spoke-level thin structures that were previously only renderable rather than reconstructable, and, as a reading of the title, to the primitive itself turning from a blob into an oriented thin element-this second reading is the author's interpretation, not a definition given in the paper.)

This paper's angle is that the obstacle comes from the primitive lacking orientation, so orientation should simply be put back into the primitive. The authors give each Gaussian a learnable unit normal \(\mathbf{n}_i\) (the only additional learnable parameter in the framework) and interpret the Gaussian as a stochastic oriented surface element: it attenuates according to the Gaussian density only in its outward half-space, while the inward side is considered fully occupied. The resulting oriented attenuation satisfies the reciprocity required by Objects as Volumes (OaV), so the OaV machinery applies directly and the occupancy, vacancy and normal fields all become closed-form expressions of the Gaussian parameters, with no MLP and no extra learnable parameters. Building on this, an image-space normal alignment loss and a normal-aware densification strategy force the Gaussians to wrap the entire surface, including extremely thin structures, into a sealed shell of oriented primitives, and two mesh extraction procedures turn the continuous fields into watertight meshes. Core idea: upgrade every 3DGS Gaussian from an orientation-free symmetric blob into an oriented surface element with a learnable normal, use its oriented attenuation to plug 3DGS into the stochastic-geometry view of Objects as Volumes, obtain closed-form occupancy and normal fields, and let those fields directly drive high-fidelity watertight mesh extraction.

Method

Overall Architecture

The input is a set of multiview RGB images with camera poses; the output is a watertight (optionally textured) triangle mesh of the full scene. The pipeline has three stages. In the training stage, fast 3DGS rasterization is kept, and each Gaussian is given a learnable oriented normal, which reinterprets it through a new oriented attenuation coefficient; the rasterizer outputs colour, depth and expected normal, where depth is not blended along the ray but obtained by exactly locating the 0.5-isosurface of the geometric field via binary search. The objective contains an image-space normal alignment loss plus a normal-aware densification: wherever the normal alignment error rises locally, the wrapping shell has a gap, so the high-error Gaussians are cloned with flipped normals to close it. In the field evaluation stage, the OaV framework turns the Gaussian parameters into a continuous Gaussian vector field \(\mathbf{V}\) and normal field \(\mathbf{N}\), both closed-form and parameter-free; a product taken over the "most unobstructed" training ray additionally provides a lower bound on the vacancy, which is inherently robust to floating Gaussians hidden inside the geometry. The mesh extraction stage offers two complementary routes: fast pivot-based Marching Tetrahedra (only two pivots per Gaussian, directly watertight, suited to whole scenes) and Primal Adaptive Meshing (region-of-interest meshing whose resolution is decoupled from the Gaussian distribution).

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    A["Multiview RGB + camera poses"] --> B["Oriented Gaussians<br/>learnable normal + oriented attenuation"]
    B --> C["Gaussian Wrapping training<br/>normal alignment loss + normal-aware densification"]
    C --> D["Lower-bound vacancy + pivot-based<br/>Marching Tetrahedra"]
    C --> E["Primal Adaptive Meshing<br/>Newton projection + Delaunay"]
    D --> F["Watertight scene mesh"]
    E --> G["ROI mesh at arbitrary resolution"]

Key Designs

1. Oriented Gaussians: give every primitive a normal and turn a blob into a surface element

As noted above, symmetric primitives contradict the asymmetry of a surface, and 3DGS opacity rendering does not line up with the attenuation coefficient that OaV requires, so the OaV closed forms are unavailable as-is. The definition is deliberately light: each Gaussian \(i\) receives a learnable unit normal \(\mathbf{n}_i\) together with an oriented attenuation coefficient that only attenuates in the outward half-space of the Gaussian, treating the inward side as fully occupied (Definition 1, Eq. (3); ⚠️ that equation is corrupted in the cached text, so refer to the original paper for the exact symbolic form). Once the attenuation is reciprocal (\(\sigma(\mathbf{x},\mathbf{w})=\sigma(\mathbf{x},-\mathbf{w})\), which is also the precondition for multiview consistency), plugging it into OaV Eq. (1) yields the paper's main result:

\[\mathbf{V}(\mathbf{x}) = \sum_{i=1}^{N} \mathbf{n}_i\bigl(-\log(1-G_i(\mathbf{x}))\bigr), \qquad \mathbf{N}(\mathbf{x}) = \frac{\mathbf{V}(\mathbf{x})}{\lVert \mathbf{V}(\mathbf{x})\rVert}\]

(⚠️ The coefficient part is corrupted in the cache; this is rewritten from the paper's semantics and should be checked against the original.) Under the OaV assumptions \(\mathbf{V}\) is a closed-form estimate of \(\nabla \log v\), so \(\mathbf{N}(\mathbf{x})\) is well defined in a neighbourhood of the surface and coincides with the true normal field of the expected stochastic surface. In practice the quantities are approximated locally by querying only the K nearest Gaussians around each point. The value of this design is that "where the surface is and which way it faces" becomes a directly evaluable continuous field, and apart from \(\mathbf{n}_i\) itself no new parameters are introduced; compared with the concurrent GGGS, which also derives a continuous transmittance from Gaussians, the oriented normal restores per-Gaussian multiview depth consistency and reciprocity, which is exactly what prevents surface erosion.

2. Gaussian Wrapping training: wrap the whole surface with normal alignment

Having a field is not enough, because the field is only valid under the premise that the Gaussians really do form a sealed shell. During training, a splatting rasterizer (the authors modify the CUDA rasterizer of GGGS) renders both depth \(D(p)\) and expected normal \(\mathbf{N}(p)\), and the rendered normal is forced to align with the image-space gradient of the depth:

\[\mathcal{L}_{\mathrm{N}} = \sum_{p} \mathbf{N}(p)\cdot\nabla D(p)\]

Since the camera-facing surface normal points toward decreasing depth, a correct \(\mathbf{N}\) is anti-parallel to \(\nabla D\), so minimizing this dot product requires each Gaussian's normal to agree with the outward normal of the surface patch it covers. Paired with this is normal-aware densification: when one side of a surface is not covered by Gaussians, the shell has a gap and \(\mathcal{L}_{\mathrm{N}}(p)\) rises locally, so every K iterations the alignment error is computed across all training views and propagated back to individual Gaussians through their blending weights; the high-error Gaussians are cloned and flipped in normal so the clone lands exactly on the missing side, closing the gap and thickening the shell. This contrasts with 3DGS's default cloning/splitting, which follows position gradients and is blind to orientation: 3DGS densification only makes the image look better, whereas this densification is driven directly by "where geometry is not wrapped", which is what makes bicycle-spoke-level structures, only one or two pixels wide, recoverable.

3. Lower-bound vacancy and pivot-based Marching Tetrahedra

The most direct way to turn the field into a mesh is to integrate \(\mathbf{V}\) along camera rays, but Gaussians that contribute nothing to rendering can remain hidden inside the geometry; a ray crossing one would violate the wrapping assumption and produce artifacts. Instead, the authors compute a lower-bound estimate \(\tilde{v}_{\mathcal{T}}\) of the vacancy from all training camera rays: for every ray through \(\mathbf{x}\), take the product of the per-Gaussian contributions at their "most unobstructed" positions (the truncated points \(t^{i}_{\mathbf{o},\mathbf{w}}=\arg\max_t G_i(\mathbf{o}+t\mathbf{w})\)), then take the maximum over all rays, i.e. the most unobstructed ray decides how vacant the point is; formally \(\tilde{v}_{\mathcal{T}}(\mathbf{x}) \le v(\mathbf{x})\) (⚠️ Eq. (7) is corrupted in the cache; this is a rewrite from the paper's semantics). This estimate has two virtues: the products can only decrease along a ray, so floating Gaussians hidden inside the geometry cannot inflate the vacancy, making the estimate inherently robust; and it formalizes the opacity-field meshing heuristics that recent works adopted empirically. On top of it, pivot-based Marching Tetrahedra is applied: under the oriented-Gaussian assumption the surface intersects each Gaussian between its centre and the low-density side, parallel to the oriented plane, so only two Delaunay pivots are needed per Gaussian-the centre \(\boldsymbol{\mu}_i\) and \(\boldsymbol{\mu}_i + 3s_i\mathbf{n}_i\), where \(s_i\) is the ellipsoid scaling along \(\mathbf{n}_i\). Occupancy values at the pivots come from \(\tilde{v}_{\mathcal{T}}\), Marching Tetrahedra runs on the resulting Delaunay triangulation, and vertices are refined to the 0.5-isosurface by binary search. Against the nine pivots per Gaussian required by prior work, cutting the count to two yields substantially lighter, fully watertight meshes without sacrificing surface fidelity-which is the direct source of the paper's "a fraction of the mesh weight of competitors" claim.

4. Primal Adaptive Meshing: decouple mesh resolution from the Gaussian distribution

Pivot-based extraction is simple and efficient, but its vertices grow directly out of the Gaussian primitives, so vertex density is dictated by the Gaussian distribution: finer meshes require more Gaussians or more pivots, and the latter merely inflates legacy metrics (the paper states explicitly that extracting with 9 pivots instead of 2 artificially raises scores). Primal Adaptive Meshing instead meshes the continuous field directly, in four iterated stages. ① Vertex initialization: sample the faces of the Marching Tetrahedra mesh, weighting each face inversely proportional to its distance from the nearest training camera, so faces close to cameras receive more vertices. ② Isosurface refinement: project vertices onto the \(\tilde{v}_{\mathcal{T}}=0.5\) isosurface with a Newton update that steps along the current normal \(\mathbf{N}(x_i)\), with a step size commensurate with how far the occupancy is from 0.5 and with the magnitude of the occupancy gradient (Eq. (8); ⚠️ corrupted in the cache, check the exact coefficients in the original). ③ Filtering: vertices with \(|0.5 - \tilde{v}_{\mathcal{T}}(x)| > \epsilon\) are treated as outliers and removed, and stages ①②③ iterate until no vertex is removed. ④ Delaunay and extraction: the remaining vertices are Delaunay-tetrahedralized, each tetrahedron is classified as inside or outside from the value of \(\tilde{v}_{\mathcal{T}}\) at randomly sampled interior points, and the final surface consists of the triangle faces separating inside from outside tetrahedra. The resulting resolution is independent of the Gaussian distribution, so a restricted segment of the scene (a stretch of bicycle spoke, say) can be meshed at arbitrary resolution; because global distance-based metrics are inherently insensitive to high-frequency detail, the gain in those metrics is limited, but smoothness improves markedly and discretization artifacts are reduced.

Loss & Training

The total loss is the sum of four terms, \(\mathcal{L} = \mathcal{L}_{\text{RGB}} + \lambda_{\text{DN}}\mathcal{L}_{\text{DN}} + \lambda_{\text{N}}\mathcal{L}_{\text{N}} + \mathcal{L}_{\text{MV}}\): \(\mathcal{L}_{\text{RGB}}\) is the standard 3DGS photometric loss, \(\mathcal{L}_{\text{DN}}\) is depth-normal consistency (following RaDe-GS/GGGS), and \(\mathcal{L}_{\text{MV}} = \lambda_{\text{pc}}\mathcal{L}_{\text{pc}} + \lambda_{\text{gc}}\mathcal{L}_{\text{gc}}\) is the multiview photometric and geometric consistency term from PGSR/GGGS. The weights are \(\lambda_{\text{DN}} = 0.05\), \(\lambda_{\text{N}} = 0.05\), \(\lambda_{\text{pc}} = 0.6\) and \(\lambda_{\text{gc}} = 0.02\). The only additional learnable parameters are the oriented normals; remaining implementation details (iteration counts, K, \(\epsilon\)) are left to the supplementary material. Note also how depth is rendered: the rasterizer does not output blended depth but locates the 0.5-isosurface of the geometric field by binary search, which is why "RaDe-GS + Gaussian Wrapping" and the full method have different numbers in the paper's tables.

Key Experimental Results

Main Results

Evaluation uses DTU and Tanks & Temples (T&T), plus the Mesh-Based Rendering (MBR) protocol introduced by MILo to assess mesh completeness and background reconstruction. The authors also identify two systematic biases in the standard protocol and propose two alternatives. (1) Legacy protocol: building the predicted point cloud from mesh vertices and face centres rewards denser tessellation-inflating scores simply by extracting with 9 pivots instead of 2-while laser-scan ground truth unfairly penalizes methods that correctly reconstruct occluded or grazing-angle surfaces. (2) Uniform Sampling uniformly samples a fixed number of points from the reconstructed mesh surface inside the GT crop volume, eliminating the vertex-density bias. (3) Virtual Scanning further simulates the acquisition process: depth maps of the reconstructed mesh are rendered from the input camera poses and back-projected into the GT crop volume. All baselines were re-run by the authors under exactly the same protocols.

F1 on T&T (mean over 6 scenes, higher is better; RM = Radiance Meshes and MS = MeshSplatting are non-Gaussian baselines; Ours (2p) is the fast two-pivot extraction, Ours (PAM) uses the Primal Adaptive Mesh):

Protocol 2DGS PGSR GOF SOF RaDe-GS MILo GGGS Ours (2p) Ours (PAM)
Uniform Sampling F1 ↑ 0.33 0.52 0.31 0.32 0.35 0.34 0.45 0.48 0.43
Virtual Scanning F1 ↑ 0.38 0.53 0.38 0.37 0.39 0.42 0.53 0.53 0.53
Training time 12 m 45 m 69 m 17 m 12 m 150 m 32 m 27 m 27 m

(2DGS and PGSR reconstruct foreground only; RM at 0.11 and MS at 0.07, with 22 m and 30 m training times, are a weaker non-Gaussian tier reported in the supplementary.) Under the unbiased Uniform Sampling protocol the method sets a new state of the art among full-scene extraction methods (0.48, above GGGS at 0.45 and MILo at 0.34). PGSR's 0.52 is an apparent outlier: its TSDF fusion and depth filtering yield non-watertight meshes whose holes coincide with those of the ground-truth scan, an artifact of the acquisition process rather than geometric quality, documented in the supplementary. Under Virtual Scanning, which explicitly simulates that acquisition bias, PGSR's advantage disappears and the method ties GGGS for a new state of the art (0.53 each).

MBR metrics (image metrics: higher PSNR/SSIM and lower LPIPS are better; M means millions; MipNeRF 360 and T&T):

Method MipNeRF360 PSNR ↑ SSIM ↑ LPIPS ↓ #Gaussians #Verts T&T PSNR ↑ SSIM ↑ LPIPS ↓ #Gaussians #Verts
2DGS 15.36 0.4987 0.4749 1.88 4.31 14.23 0.5697 0.4854 0.98 16.39
PGSR 15.63 0.5834 0.4509 3.16 22.78 14.55 0.5956 0.4819 1.47 11.79
GOF 24.25 0.7017 0.3454 2.99 32.80 20.10 0.6475 0.4073 1.25 11.63
RaDe-GS 24.84 0.7291 0.3128 2.91 30.85 20.70 0.6767 0.3876 1.18 10.06
MILo 25.075 0.7339 0.3096 0.46 6.73 21.198 0.6908 0.3782 0.28 4.36
GGGS 24.55 0.7386 0.2986 4.08 43.46 20.70 0.6912 0.3734 1.73 21.81
Ours 25.10 0.752 0.289 4.0 11.79 20.98 0.7004 0.3674 2.07 5.80

Worth noting is the mesh weight at comparable accuracy: on MipNeRF 360 the method reaches 25.10 PSNR with 11.79 M vertices, while GGGS needs 43.46 M vertices for 24.55; on T&T the figures are 5.80 M versus 21.81 M. For DTU the paper reports conclusions only (the Chamfer Distance over 15 scenes is in the supplementary): competitive with GGGS and better than foreground-only methods such as 2DGS and PGSR, and crucially without the surface erosion artifacts of GGGS. Novel view synthesis on Mip-NeRF 360 is also competitive and sets a new state of the art for outdoor scenes (details in the supplementary). Two honest caveats: MILo attains higher PSNR than this method on T&T (21.198 vs 20.98) with far fewer Gaussians and vertices, so "more compact" here is relative to GOF/GGGS/RaDe-GS; and the full DTU Chamfer numbers and NVS details could not be read from the cache, so refer to the supplementary material.

Ablation Study

Component ablation (T&T, mean over 6 scenes; Mesh Qual. is the legacy vertex-based F1, reported alongside Virtual Scan F1):

Config Virtual Scan F1 ↑ Mesh Qual. F1 ↑ PSNR ↑ SSIM ↑ LPIPS ↓
Baseline (no Gaussian Wrapping) 0.53 0.48 20.74 0.6958 0.3718
+ Normal Alignment Loss 0.52 0.48 20.78 0.6986 0.3683
+ Normal Alignment Loss + Densification (full) 0.53 0.48 20.98 0.7004 0.3674

Generalization as a drop-in regularizer (Gaussian Wrapping plugged into RaDe-GS, Virtual Scan F1 per T&T scene):

Config Barn Caterpillar Courthouse Ignatius Meetingroom Truck Mean
RaDe-GS 0.47 0.30 0.11 0.66 0.25 0.57 0.39
RaDe-GS + Gaussian Wrapping 0.63 0.46 0.13 0.71 0.34 0.60 0.48

Key Findings

  • Geometric and rendering metrics measure different things. Adding the normal alignment loss leaves both T&T F1 scores essentially unchanged (0.53 → 0.52 → 0.53) while MBR metrics improve steadily (SSIM 0.6958 → 0.6986 → 0.7004, LPIPS 0.3718 → 0.3683 → 0.3674, PSNR 20.74 → 20.78 → 20.98). The reason is stated bluntly: the rasterizer already places Gaussians near the isosurface, so global distance-based F1 only measures coarse alignment and cannot measure detail fidelity-and the normal alignment loss is precisely what rescues fine detail (thin structures, sharp edges); without it they are lost. This doubles as a critique of the T&T ground truth and metric themselves.
  • Densification and normal alignment play complementary roles. With the alignment loss alone, Virtual Scan F1 even dips slightly (0.53 → 0.52), showing that aligning orientation is not enough and densification must still cover the missing side; only the two together push the MBR metrics into place.
  • Gaussian Wrapping is portable. Plugged into RaDe-GS it improves every T&T scene (mean 0.39 → 0.48; Barn 0.47 → 0.63, Caterpillar 0.30 → 0.46), confirming that it does not depend on this paper's depth rasterization and is itself an effective geometric regularizer. The remaining gap between "RaDe-GS + GW" and the full method comes from how depth is rendered (whether the 0.5-isosurface is located by binary search).
  • PGSR's strong geometric scores are an artifact of the protocol. Under Uniform Sampling it wins through a hole-for-hole coincidence with the ground truth, under Virtual Scanning its advantage vanishes, and the MBR metrics expose the background holes left by its depth filtering (MipNeRF 360 PSNR of only 15.63, far below the 24-plus of full-scene methods).
  • The two extraction routes serve different purposes. Ours (2p) is stronger in the globally uniform sampling evaluation (0.48 vs 0.43), whereas the Primal Adaptive Mesh earns its keep not in global metrics but in meshing regions of interest at arbitrary resolution with cleaner topology (local comparisons on bicycle and bonsai are given in Fig. 4 of the paper).

Highlights & Insights

  • Adding primitive orientation solves two problems at once. A single learnable normal simultaneously acts as (a) the reciprocity fix for the rendering model and (b) the definition of an implicit geometric field, so "can we use OaV" and "are depths multiview-consistent" - previously separate concerns - are resolved by one degree of freedom. This "trade a minimal parameter increment for a theoretical interface" move transfers well: whenever a particle-based representation wants to hook into a continuous-field theory (OaV, implicit fields, differentiable rendering), first ask whether what is missing is the primitive's orientation or sign.
  • The error signal is used as a geometric probe rather than just a loss. Regions where the normal alignment loss rises are exactly where the shell has broken, and instead of merely minimizing it the authors propagate it back to Gaussians as a cloning/flipping criterion-training loss doubles as a densification scheduler. This recycling of a diagnostic signal is a broadly reusable trick.
  • The critique of the evaluation protocol is a hidden contribution. "Vertices plus face centres as a point cloud → rewards dense tessellation" and "laser ground truth punishes methods that correctly reconstruct occluded regions" are traps anyone working on Gaussian-based surface reconstruction has hit; Uniform Sampling and Virtual Scanning are lightweight patches that flip conclusions (PGSR goes from "strongest" to "protocol artifact"). Both are directly transferable to any laser-scan-based geometric benchmark.
  • Nine pivots become two. Because the oriented assumption makes it known on which side the surface intersects each Gaussian, extra pivots are unnecessary. This is a clean case of "a stronger prior buys a cheaper representation": the prior pays out as smaller meshes and faster extraction.

Limitations & Future Work

  • The authors acknowledge that Primal Adaptive Meshing currently relies on uniform sampling of the initial MTet mesh, which can be suboptimal for highly detailed scenes; guiding the sampling with the Gaussian vector field or local curvature is a promising extension. The method is not tailored to specular, transparent or sky regions, where the reconstructed surface may be deformed or absent (examples in the supplementary), and Marching Tetrahedra guarantees watertightness but not correctness. The authors also note that the attenuation-based formulation is not tied to 3DGS and could extend to more accurate volumetric rendering models such as EVER, and that the local vacancy defined by \(\mathbf{V}\) could in turn be supervised directly-this paper only uses it as a derived quantity.
  • On assumptions: everything rests on a binary, fully opaque scene (each point either inside or outside), so semi-transparent, mirror-like, foliage and fur scenes are outside its scope in principle. The equivalence between the oriented attenuation and the 3DGS image formation model also relies on approximations such as primitives not overlapping in 3D (proved in the supplementary); how large the error of that equivalence becomes in densely overlapping regions (on T&T this method uses more Gaussians than GGGS, 2.07 M vs 1.73 M) is not quantified in the main text.
  • Honest numerical caveats: the DTU Chamfer Distance and the Mip-NeRF 360 NVS details live in the supplementary, so the claims "competitive on DTU" and "state of the art on outdoor NVS" cannot be cross-checked within the main paper; on MBR metrics MILo attains higher T&T PSNR with a lighter representation (0.28 M Gaussians / 4.36 M vertices), so this method's edge lies mainly in MipNeRF 360 and in SSIM/LPIPS.
  • Improvement directions: supervise \((1-\tilde{v})\) directly as a differentiable occupancy target for the Gaussians (the authors' own suggestion, which would make the field more self-consistent); replace PAM's uniform initial sampling with sampling driven by \(\mathbf{V}\) or curvature; and extend the oriented attenuation from 3DGS to more accurate ellipsoid renderers such as EVER, or replace the current lower-bound vacancy with a tighter upper bound to reduce bias.
  • vs 3DGS + TSDF methods (PGSR, GOF, RaDe-GS, 2DGS): they all regularize within the opacity rendering framework and extract via density thresholds or TSDF fusion of blended depth, with no principled link between Gaussian parameters and a geometric field. Consequently they either produce non-watertight meshes with background holes (PGSR) or enormous meshes (GOF, 32.80 M vertices). This paper supplies the missing link: it first derives closed-form occupancy and normal fields, then lets extraction consume those fields directly.
  • vs 2DGS and lower-dimensional / triangle-primitive routes: 2DGS replaces 3D primitives with lower-dimensional surfels for better geometric consistency, but it changes the dimensionality of the primitive, not its orientation semantics, and it still has no global geometric field, so TSDF remains necessary. Replacing primitives with triangles outright (the Triangle Splatting line of work) is a different branch of explicit meshing; this paper does not compare against such methods directly, ⚠️ so any claim there should be checked against the original. As far as this paper goes, the difference is that it keeps Gaussian primitives unchanged and merely adds a normal, so it retains the real-time rendering and densification machinery of 3DGS.
  • vs GGGS (concurrent and closest): both derive a continuous transmittance/attenuation from Gaussians to improve depth, but GGGS does not enforce multiview-consistent depth for a single Gaussian, which produces surface erosion and detail loss; the oriented normal restores reciprocity and consistency, suppresses erosion and supports a well-defined occupancy field. On T&T the two tie on Virtual Scanning F1 (0.53 each), but this paper's meshes are far lighter.
  • vs GOF / MILo (pivot and Delaunay routes): GOF and MILo also use Delaunay pivots for watertight meshes, but need nine pivots per Gaussian and derive their field from a heuristic opacity threshold. This paper needs only two pivots (the oriented assumption directly gives where the surface intersects each Gaussian) and formalizes the previously empirical "mesh the opacity field" heuristic via the lower-bound vacancy. MILo keeps a rendering prior and is therefore competitive on MBR metrics; this paper has no such prior yet surpasses it on MipNeRF 360.
  • vs implicit SDF methods (NeuS, VolSDF, Neuralangelo) and neural-kernel approaches (e.g. Neural Kernel Surface Reconstruction): implicit routes give continuous, topologically consistent surfaces but need hours of training (RM requires 378 minutes in the paper's table) and come out over-smoothed, with high-frequency detail absorbed by the smoothness of the MLP or kernel regression. This paper's fields are closed-form, given directly by the hundreds of thousands to millions of Gaussian parameters, needing neither an MLP nor a per-scene network-the price is the premise that the Gaussians wrap the surface well enough. ⚠️ The paper does not compare against NKS-style neural-kernel methods directly; this comparison is at the level of method families.

Rating

  • Novelty: ⭐⭐⭐⭐⭐ Plugging a single extra degree of freedom-primitive orientation-into Objects as Volumes buys closed-form occupancy and normal fields plus a self-consistent extraction pipeline; theoretically clean and parameter-frugal.
  • Experimental Thoroughness: ⭐⭐⭐⭐ Two datasets, three evaluation protocols, a component ablation and a cross-method generalization study, plus a deliberate fix of the evaluation protocol; the weakness is that key DTU and NVS numbers sit in the supplementary and cannot be cross-checked from the main text.
  • Writing Quality: ⭐⭐⭐⭐ The motivation chain (symmetric blob vs asymmetric surface; opacity vs unbounded attenuation) is exceptionally clear and the critique of evaluation bias is concrete; the cost is a cramped rendering of the core equations and repeated reliance on the supplementary.
  • Value: ⭐⭐⭐⭐⭐ It provides a reusable regularizer for everyone extracting surfaces from Gaussians (proved portable by RaDe-GS + GW) and the first watertight extraction scheme requiring only two pivots per Gaussian, with high practical value.