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

Diego Gomez; Antoine Guédon; Nissim Maruani; Bingchen Gong; Maks Ovsjanikov

cs.CVApr 8, 2026

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

Authors: Diego Gomez, Antoine Guédon, Nissim Maruani, Bingchen Gong, Maks Ovsjanikov

Organizations: LIX, École Polytechnique, France · Inria, Côte d’Azur, France

Abstract

3D Gaussian Splatting (3DGS) has revolutionized fast novel view synthesis, yet its opacity-based formulation makes surface extraction fundamentally difficult. Unlike implicit methods built on Signed Distance Fields or occupancy, 3DGS lacks a global geometric field, forcing existing approaches to resort to heuristics such as TSDF fusion of blended depth maps. Inspired by the Objects as Volumes framework, we derive a principled occupancy field for Gaussian Splatting and show how it can be used to extract highly accurate watertight meshes of complex scenes. Our key contribution is to introduce a learnable oriented normal at each Gaussian element and to define an adapted attenuation formulation, which leads to closed-form expressions for both the normal and occupancy fields at arbitrary locations in space. We further introduce a novel consistency loss and a dedicated densification strategy to enforce Gaussians to wrap the entire surface by closing geometric holes, ensuring a complete shell of oriented primitives. We modify the differentiable rasterizer to output depth as an isosurface of our continuous model, and introduce Primal Adaptive Meshing for Region-of-Interest meshing at arbitrary resolution. We additionally expose fundamental biases in standard surface evaluation protocols and propose two more rigorous alternatives. Overall, our method Gaussian Wrapping sets a new state-of-the-art on DTU and Tanks and Temples, producing complete, watertight meshes at a fraction of the size of concurrent work-recovering thin structures such as the notoriously elusive bicycle spokes.

Figures & tables

Figure 1: High-fidelity surface reconstruction from 3D Gaussian Splatting. Our method, Gaussian Wrapping, reconstructs watertight and textured surface meshes of full 3D scenes given multiview RGB images, by interpreting 3D Gaussians as stochastic oriented surface elements. This figure illustrates the resulting surface meshes, with and without the RGB texture. Our meshes represent the full scene—including background geometry and extremely thin structures such as bicycle spokes where existing methods fail—with a significantly more compact representation than concurrent works [ 57 , 10 ] .

Panel of Figure 2 — Figure 2: Examples of textured meshes reconstructed with our method. While being watertight and lighter than meshes reconstructed by state-of-the-art methods, our approach is able to reconstruct extremely fine details such as a few blades of grass—as can be seen in the close-up view of the stump scene [ 5 ] .

Figure 3: Wrapping the surface with Oriented Gaussians. Our Gaussian Wrapping setting allows to evaluate the normal and vacancy fields of the scene. We first leverage the vacancy on our pivot-based marching tetrahedra meshing approach. We then leverage both the vacancy and normal fields in our Primal Adaptive Meshing.

Panel of Figure 4 — Figure 4: Primal Adaptive Meshing on restricted scene segments. Close-up comparisons between our standard Pivot-based MTet extraction (a) and the Primal Adaptive Mesh (b) applied to the same segment on the bicycle and bonsai scenes of the MipNeRF 360 dataset. The Primal Adaptive Mesh produces topologically clean surfaces that faithfully reflect the underlying Gaussian isosurface.

Uniform Sampling Evaluation
	Foreground only			Full scene extraction
	2DGS	PGSR	Ours (PAM)	GOF	SOF	RaDe-GS	MILo	GGGS	Ours (2p)
Barn	0.48	0.65	0.63	0.40	0.45	0.42	0.40	0.57	0.64
Caterpillar	0.24	0.45	0.38	0.23	0.20	0.22	0.24	0.41	0.41
Courthouse	0.13	0.24	0.07	0.10	0.07	0.12	0.11	0.10	0.19
Ignatius	0.51	0.81	0.76	0.55	0.68	0.66	0.72	0.79	0.77

Table 1: Quantitative comparison on the Tanks & Temples Dataset [ 27 ] . F1 scores under two complementary evaluation protocols. Uniform Sampling : points are uniformly sampled from the mesh surface, eliminating vertex-count bias. Virtual Scanning : depth maps are back-projected from the original camera viewpoints, mirroring the ground truth acquisition process. We report average training time.

Foreground only
	MipNeRF 360					Tanks & Temples
	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	#Gaussians $\downarrow$	#Verts $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	#Gaussians $\downarrow$	#Verts $\downarrow$
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
Full scene extraction
GOF	24.25	0.7017	0.3454	2.99	32.80	20.10	0.6475	0.4073	1.25	11.63

Table 2: Mesh-Based Novel View synthesis metrics on real-world datasets . We report PSNR, SSIM, and LPIPS metrics, as well as the total number of Gaussians and vertices (in millions). Our method demonstrates superior performance on these challenging unbounded scenes.

Component Ablation (Mean across scenes)
	F1-Score $\uparrow$		MBR Metrics
Configuration	Virt. Scan	Mesh Qual.	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Baseline	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	0.53	0.48	20.98	0.7004	0.3674

Table 3: Ablation studies on Tanks & Temples. Top : Mean scores across all scenes for our component ablation, reporting F1-score under both evaluation protocols and Mesh-Based Rendering (MBR) metrics. Bottom : Per-scene Virtual Scan F1-score demonstrating that our contributions generalize as a plug-in regularizer to RaDe-GS [ 56 ] . The normal alignment loss and densification procedure constitute the Gaussian Wrapping approach.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 6 — Figure 6: Comparison between our continuous attenuation model, and the one proposed in GGGS [ 57 ] . Top figure: The sphere illustrated on the left (a) represents the $0.5$ -isosurface of a single isotropic Gaussian. Given a camera located below the Gaussian and looking up, we represent the corresponding $0.5$ -isosurface of the transmittance for both our continuous attenuation model (b) and GGGS [ 57 ] (c). Our method produces unbiased, spherical isosurfaces aligned with the visible part of the actual Gaussian isosurface. On the contrary, GGGS produces non-multi-view consistent surfaces misaligned with the Gaussian isosurface, leading to erosion. Bottom row illustrates the actual RGB rendering, depth maps and normal maps obtained for both methods.

Panel of Figure 7 — Figure 7: Equivalence between Gaussian Splatting rendering and our attenuation-based formulations. (a) Standard Gaussian Splatting rasterization. (b) Ray-marching our derived attenuation field from Equation 18 , with corresponding error map. (c) Ray-marching the oriented attenuation after optimizing Gaussians with our oriented normal regularization 4 . Both attenuation-based models produce visually similar results, confirming the formal equivalence established in Sec. 0.B.1 and the approximation proposed in Sec. 0.B.2 . The discrepancies occur precisely when the non-overlapping conditions aren’t met, such as the poorly supervised background.

Panel of Figure 8 — Figure 8: Evolution of the vacancy along a ray. In contrast to the initial attenuation we derived for Gaussian Splatting (a), our oriented Gaussian formulation (b) allows for a reciprocal formulation of the vacancy. This figure shows how our formulation corrects the bias present in (a). Indeed, in (a) vacancy starts changing just before each Gaussian. This poses a problem for $G_{2}$ , since vacancy starts evolving from occupied to empty before crossing $t_{o,w}^{G_{2}}$ . You can see in that in our formulation (b) this change happens after crossing this critical point. This renders the evaluation of vacancy reciprocal

Panel of Figure 9 — Figure 9: Gaussian vector field aligned with surface normals. Visualization of the Gaussian normal field $\mathcal{N}$ , i.e . the normalized vector field $V=\nabla\log v$ , across four scenes (Kitchen, Room, Ignatius, Courthouse). Each row shows, from left to right: the ground truth RGB image, the normals rendered by alpha-blending the oriented Gaussian normals $n_{i}$ , and the normal field $\mathcal{N}(x)$ queried at points $x$ lying on the 0.5-isosurface of the transmittance (median depth). In practice, $\mathcal{N}(x)$ is evaluated by querying the $K$ -nearest Gaussians to $x$ ( $K=32$ ). The close agreement between rendered normals and $\mathcal{N}$ confirms that the Gaussian vector field is well-aligned with the surface. We note that artifacts in the normal field $\mathcal{N}$ correspond to under-reconstructed parts of the scene (e.g specular spot on Kitchen table, TV in room, background in Ignatius scene, and sky in Courthouse scene).

Figure 10: Effect of the Newton projection step on vacancy values at sampled points. Left: Reference image with a mark on zoomed area. Top: mesh renders of the Baseline and our proposed method on the Truck scene of T&T. Bottom: distribution of vacancy values $v(x)$ evaluated at the points to refine for PAM (zoomed in on the $[0.45,0.55]$ range around the target isosurface $v=0.5$ ). This plot was obtained performing PAM on the Ignatius scene of T&T, sampling 3 Million points and performing 10 refinement steps. Bottom Left (blue): Sampled points on mesh without Newton refinement; Bottom Right (red): after applying our Newton projection step (Proposition 5 ), points collapse onto the isosurface $v=0.5$ , validating the efficiency of our refinement. Qualitatively we can see that disentangling the vertex distribution from the Gaussians distributions allows to retrieve extremely fine-grained details.

Panel of Figure 11 — Figure 11: Qualitative mesh renders on DTU. Mesh renders of our method on three DTU scenes.

Panel of Figure 12 — Figure 12: T&T evaluation shortcomings on the Caterpillar scene. The standard Tanks & Temples ground-truth point cloud (left) contains holes due to occlusion and unfavorable acquisition angles—these are limitations of the LiDAR acquisition, not of the reconstruction. PGSR (center) produces a mesh with holes that align with GT gaps, which inflates its F1 score. Our method (right) reconstructs a more complete surface shell, which can be penalized by the evaluation metric in these under-observed regions. Note that there is no GT mesh, instead for visualization purposes we use the Points to Mesh Blender functionality to render the GT point cloud.

Figure 13: Evaluation Code of T&T used by the literature [ 55 , 56 , 10 , 23 ] The traditional evaluation script uses the vertices and face center points from the mesh and uses them to build a point cloud. This way of constructing a prediction point cloud biases the metric towards dense meshes.

	Implicit						Explicit
	Gaussian UDF	GS-Pull	GSDF	NeuS	Geo-Neus	Neuralangelo	SuGaR	3DGS	2DGS	GOF	RaDe-GS	QGS	VCR-GauS	MILo (GOF base)	Ours (2p)	Ours (9p)
Barn	0.27	0.60	0.16	0.29	0.33	0.70	0.14	0.13	0.36	0.51	0.43	0.43	0.62	0.59	0.58	0.65
Caterpillar	0.17	0.37	0.11	0.29	0.26	0.36	0.16	0.08	0.23	0.41	0.32	0.31	0.26	0.39	0.48	0.50
Courthouse	0.03	0.16	OOM	0.17	0.12	0.28	0.08	0.09	0.13	0.28	0.21	0.26	0.19	0.29	0.30	0.35
Ignatius	0.38	0.71	0.34	0.83	0.72	0.89	0.33	0.04	0.44	0.68	0.69	0.79	0.61	0.78	0.70	0.75
Meetingroom	0.17	0.22	0.01	0.24	0.20	0.32	0.15	0.01	0.16	0.28	0.25	0.25	0.19	0.26	0.33	0.39

Appendix

Table 4: Legacy quantitative comparison on the Tanks & Temples dataset [ 27 ] using the standard vertex-based metric. We report F1-score and average optimization time. All results besides ours are taken from the MILo paper. When a method fails due to out-of-memory errors, we report the mean over successful scenes, denoted by a superscript asterisk (

x^{*}

). Despite the known bias of this metric (see Fig. 13 )—vertex-based sampling non-uniformly queries the isosurface in proportion to mesh density—our method achieves the best F1 score among all representations. The sensitivity of this metric to mesh density is further evidenced by the significant score increase obtained simply by adding more pivot points.

		24	37	40	55	63	65	69	83	97	105	106	110	114	118	122	Mean
implicit	NeRF [ 38 ]	1.90	1.60	1.85	0.58	2.28	1.27	1.47	1.67	2.05	1.07	0.88	2.53	1.06	1.15	0.96	1.49
	VolSDF [ 51 ]	1.14	1.26	0.81	0.49	1.25	0.70	0.72	1.29	1.18	0.70	0.66	1.08	0.42	0.61	0.55	0.86
	NeuS [ 50 ]	1.00	1.37	0.93	0.43	1.10	0.65	0.57	1.48	1.09	0.83	0.52	1.20	0.35	0.49	0.54	0.84
	Neuralangelo [ 29 ]	0.37	0.72	0.35	0.35	0.87	0.54	0.53	1.29	0.97	0.73	0.47	0.74	0.32	0.41	0.43	0.61
explicit	3D GS [ 25 ]	2.14	1.53	2.08	1.68	3.49	2.21	1.43	2.07	2.22	1.75	1.79	2.55	1.53	1.52	1.50	1.96
	SuGaR [ 19 ]	1.47	1.33	1.13	0.61	2.25	1.71	1.15	1.63	1.62	1.07	0.79	2.45	0.98	0.88	0.79	1.33

Appendix

Table 5: Surface reconstruction metrics on the DTU dataset . We report the Chamfer Distance across 15 scenes. Our method achieves competitive performance on object-centric scenes, while being able to recover very fine details in unbounded scenes.

	Indoor Scenes			Outdoor Scenes
	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
3DGS [ 25 ]	30.41	0.920	0.189	24.64	0.731	0.234
Mip-Splatting [ 54 ]	30.90	0.921	0.194	24.65	0.729	0.245
BakedSDF [ 52 ]	27.06	0.836	0.258	22.47	0.585	0.349
SuGaR [ 19 ]	29.43	0.906	0.225	22.93	0.629	0.356
2DGS [ 44 ]	30.40	0.916	0.195	24.34	0.717	0.246

Appendix

Table 6: Quantitative results for novel view synthesis on MipNeRF 360 [ 5 ] . We report PSNR, SSIM, and LPIPS. Our method maintains competitive rendering quality while significantly improving surface reconstruction.

Panel of Figure 14 — Figure 14: Ablation of the normal field loss $\mathcal{L}_{\text{N}}$ and densification on the Barn and Truck scenes. On the Barn scene, we see that by extracting a mesh with 2 pivots without our alignment loss $\mathcal{L}_{N}$ , several artifacts are present. These come in the form of large triangles that stem from a bad orientation of the Gaussians which result in bad placement for the pivots. Then below, we ablate the need for our densification (Ours = Baseline + $\mathcal{L}_{N}$ + Densification), we can see that it allows to solve for complex and poorly supervised geometry such as in between the bench slats in the bicyle scene.

Panel of Figure 15 — Figure 15: Qualitative effect of Normal Field (NF) supervision on RaDe-GS. Adding our NF losses and densification to RaDe-GS yields more faithful geometry. For instance, we mititage the erosion of the bike lock in the Barn scene, and avoid holes in the wheel of the Caterpillar scene. This shows our approach can be used to improved other existing methods.

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3D Gaussian Splatting (3DGS) has recently enabled real-time novel view synthesis with impressive quality. However, it struggles to recover accurate surfaces under limited viewpoints and due to the inherent irregularity of Gaussian primitives. The resulting geometric errors are notoriously difficult to correct manually. To address these issues, we propose Gaussian Sculpting, a fully differentiable end-to-end framework for high-quality surface reconstruction. Our key insight is to anchor Gaussians onto an evolving differentiable surface, allowing them to guide signed distance field (SDF) optimization instead of extracting the surface only during post-processing. To enable stable gradient isolation during joint optimization, we design a bi-level training strategy in which the outer loop optimizes the geometry represented by the SDF, while the inner loop updates the Gaussians with the geometry fixed. We further impose constraints on Gaussian parameters to ensure consistency with the underlying surface, thereby improving both geometric and appearance fidelity during optimization. In addition, we introduce a multi-resolution subdivision scheme based on octree-like partitioning to preserve fine details while reducing memory consumption. Experiments on object-level scenes demonstrate that our method effectively removes redundant surfaces, recovers missing structures caused by limited viewpoints, and achieves strong reconstruction quality even at relatively low resolutions.

Abstract

3D Gaussian Splatting

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