ADELE - Adaptive Delaunay Grids for High-Fidelity Mesh-Native Reconstruction

Johannes Weidenfeller; Shaofei Wang; Philipp Fürnstahl; Siyu Tang

cs.CVSep 6, 2026

ADELE - Adaptive Delaunay Grids for High-Fidelity Mesh-Native Reconstruction

Authors: Johannes Weidenfeller, Shaofei Wang, Philipp Fürnstahl, Siyu Tang

Organizations: ETH Zurich, Zurich, Switzerland · Beijing Institute for General Artificial Intelligence, Beijing, China · University of Zurich, Zurich, Switzerland · Balgrist University Hospital, Zurich, Switzerland

Abstract

Meshes remain the most practical representation for geometry reasoning and integration into graphics pipelines, yet existing reconstruction methods struggle to produce high-quality meshes. Most state-of-the-art approaches initially learn an intermediate representation (NeRF/3DGS) and treat mesh extraction as a post-processing step, which often leads to oversmoothed surfaces or poor quality meshes with excessive triangle counts.Existing mesh-native optimization methods alleviate some of these issues but suffer from fixed-resolution discretizations and unstable optimization behavior. In this paper, we introduce an adaptive mesh-based optimization framework and a practical mesh rendering technique to address these challenges. Our representation combines an optimizable Delaunay-triangulated tetrahedral grid with a multi-resolution hash grid. The former is refined through point pruning and insertion, while the latter provides latent features for SDF/appearance value predictions. We use volumetric rendering to bootstrap a coarse geometry while leveraging mesh-based rendering for recovering fine-grained details. Additionally, we propose a differentiable, rasterization-based depth-offset rendering formulation, reducing geometric artifacts and improving reconstruction quality. Our method significantly outperforms existing mesh optimization approaches across a variety of object-centric benchmarks while being competitive with state-of-the-art NeRF/3DGS methods.

Figures & tables

Figure 1. Qualitative comparison of mesh reconstructions from multi-view images. Existing methods based on 3D Gaussian Splatting (PGSR, 2DGS) or mesh-gaussian-hybrid optimization (MiLO) produce meshes with noticeable artifacts or oversmoothed surfaces. Our method directly optimizes a locally refinable tetrahedral grid with a novel depth-offset rendering formulation, yielding high-quality meshes with sharp geometric details and well-distributed triangles.

Figure 2. Overview of our framework. We represent scene geometry using an adaptive tetrahedral grid whose connectivity is maintained via Delaunay triangulation (§ 3.1 ) and whose vertex positions are optimizable (§ 3.2 ). SDF values at grid vertices are queried from a multi-resolution hash grid, and a mesh is extracted using the Marching Tetrahedra algorithm (DMTet). The mesh is rasterized via NVDiffrast to obtain depth and normal maps. For each pixel, we perform depth-offset sampling (§ 3.4 ) to generate multiple 3D sample points $\mathbf{x}_{i}$ around the surface. These points, along with the viewing direction $\mathbf{d}$ and surface normal $\mathbf{n}$ , are fed through an appearance hash grid and a color MLP to produce pixel colors. During early training, a volumetric rendering branch (dashed blue) provides additional supervision to stabilize optimization (§ 3.3 ). The final output is supervised with an $\mathcal{L}_{1}$ photometric loss against ground-truth images along with mask and mesh regularization losses (§ 3.5 ).

Figure 3. Adaptive tetrahedral grid optimization. Starting from a uniform initialization (left), the grid progressively adapts to the scene geometry through Delaunay-site (i.e. , vertex) movement, densification, and pruning. Periodic Delaunay re-triangulation maintains valid grid connectivity throughout optimization.

Figure 4. Depth-offset sampling. Per-pixel alignment between the RGB reconstruction loss gradient w.r.t. mesh position and the viewing direction for different numbers of offset samples $N$ . Red indicates strong alignment with the viewing direction, while blue denotes largely perpendicular gradients. Increasing $N$ leads to progressively stronger alignment with the viewing direction.

		24	37	40	55	63	65	69	83	97	105	106	110	114	118	122	Mean	Time
implicit	NeRF ( Mildenhall et al., 2020 )	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	$>12h$
	VolSDF ( Yariv et al., 2021 )	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	$>12h$
	NeuS ( Wang et al., 2021 )	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	$>12h$
	Neuralangelo ( Li et al., 2023 )	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	$>12h$
Gaussian	3DGS ( Kerbl et al., 2023 )	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	11.2 m
	SuGaR ( Guédon and Lepetit, 2024b )	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	$\sim$ 1h

Table 1. Quantitative comparison of geometric reconstruction on the DTU dataset. We report Chamfer distance (mm,

\downarrow

) for 15 test scenes, grouped by representation type: implicit (NeRF-based), Gaussian (3DGS-based), and mesh-based methods. Colors indicate 1st , 2nd , and 3rd place per scene. Our method achieves lower mean Chamfer distance among mesh-based approaches while performing on par with state-of-the-art radiance-field methods. Baseline runtimes are from ( Guédon et al., 2025a ) (RTX 4090, 24 GB); ours were measured on an H200 (141 GB)*.

Method	Basketball	Bear	Bread	Camera	Clock	Cow	Dog	Doll	Dragon	Durian	Fountain	Gundam	House	Jade	Man	Monster	Sculpture	Stone	Mean
NeuS	2.96	3.00	2.85	2.61	2.75	2.04	2.75	2.17	2.95	3.14	3.03	1.62	3.23	4.25	2.29	1.92	2.10	2.51	2.68
Surfels	1.59	1.52	1.41	1.75	5.08	3.21	2.97	2.32	2.93	4.01	2.65	0.97	1.76	3.49	2.23	1.36	3.07	2.02	2.46
SuGar	8.00	9.73	7.65	7.77	9.21	8.69	9.27	8.75	9.76	8.04	9.05	7.32	7.28	10.7	9.29	8.20	8.98	9.19	8.71
PGSR	0.92	1.05	0.74	1.51	1.64	1.09	1.35	1.33	1.51	1.63	1.50	0.92	1.18	3.01	1.17	0.97	1.25	1.08	1.35
IMLS-Splatting	2.48	1.86	2.69	3.61	2.96	2.80	2.85	2.32	2.39	3.35	2.83	1.78	3.01	5.10	2.61	1.99	2.04	2.85	2.75
Mesh Splatting	1.26	1.16	0.75	1.75	1.99	1.30	2.08	2.02	1.57	2.36	2.37	0.90	1.94	3.27	1.52	1.30	1.64	1.64	1.71

Table 2. Quantitative comparison of geometric reconstruction on the BlendedMVS dataset. We report Chamfer distance (mm,

\downarrow

) for 18 test scenes. Colors indicate 1st , 2nd , and 3rd place per scene. Our method achieves the best mean Chamfer distance among mesh-based methods.

Figure 5. Qualitative comparison on the DTU dataset. We compare mesh reconstructions on two challenging scenes. 2DGS and MiLO produce oversmoothed surfaces that lose geometric detail. PGSR captures some details but exhibits surface noise. Our method reconstructs sharp edges and high-frequency details while maintaining clean mesh quality, as visible in the roof tiles and the bird’s textured feathers.

		PSNR $\uparrow$
Render	Method	Chair	Drums	Ficus	Hotdog	Lego	Mats.	Mic	Ship	Avg
Native	PGSR	31.62	24.69	28.60	35.09	31.67	28.93	33.81	29.14	30.44
	MILo	32.69	25.52	34.67	34.82	33.77	29.11	33.51	30.76	31.85
	NVDiffrec	31.60	24.10	30.88	33.04	29.14	26.74	30.78	26.12	29.05
	Ours	31.68	24.42	29.48	34.00	30.79	26.41	32.25	28.43	29.68
Mesh	PGSR	27.12	16.40	22.13	29.60	27.41	14.86	24.95	24.69	23.40

Table 3. Quantitative comparison on NeRF Synthetic. PSNR (

\uparrow

) and SSIM (

\uparrow

) under two rendering protocols: Native rendering uses each method’s own renderer (3DGS for PGSR/MiLO, neural-shaded mesh rasterization for ours); Extracted-mesh rendering renders the extracted mesh shaded with a per-vertex diffuse albedo.

Configuration	DTU ↓	BMVS ↓
Full Model (ours)	0.53	1.47
w/o Mesh-Based Rendering	0.79	3.17
w/o Hybrid Training	0.72	1.98
w/o Densification	0.59	5.37
w/o Offset Sampling	0.55	1.56

Table 4. Ablation studies on the DTU and BMVS datasets. We report the Chamfer Distance (↓) for different variants of our method on both datasets.

Figure 6. Examples of mesh reconstructions obtained with our method on the TnT dataset.

Figure 7. Qualitative comparison on the BlendedMVS dataset. For each scene, we show the ground truth image, our rendered image, our predicted mesh normals, and mesh reconstructions from our method, PGSR, and MiLO. Our method produces detailed meshes that faithfully capture object silhouettes and detailed surface normals. PGSR produces overly smooth surfaces, while MILo suffers from high frequency artefacts. Best viewed zoomed in.

Figure 8. Ablational results on scenes of the DTU and BlendedMVS datasets. The top row shows results produced by our full method, while the bottom row presents results from different ablation variants.

Figure 9. Qualitative comparison on the NeRF Synthetic dataset. We compare mesh reconstructions from NVDiffrec, MILO, PGSR, and our method. NVDiffrec produces noisy surfaces with limited geometric detail. MILO reconstructs more detailed meshes but exhibit artifacts around the object silhouette. PGSR is lacking fine-grained details and additionally suffers from missing geometry due to its post processing steps. Our method recovers fine-grained geometry, such as individual leaves and the microphone grille, while maintaining clean surface quality.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 10. Depth-offset sampling. (Left) We sample multiple points along each camera ray by performing inverse sampling with respect to the opacity function $\Psi(t)$ . The sigmoid shape of $\Psi$ concentrates samples near the mesh surface, where the SDF transitions through zero. (Right) early stage reconstruction rendered using sampled depth offsets.

Figure 11. Initialization Examples. Visualizations of the coarse initial meshes derived from VGGT depth priors, which serve as the base geometry for our residual learning framework.

Figure 12. Incorporating a triangle regularization term that penalizes deviations from regular triangles in the output mesh leads to a more evenly tesselated reconstructed surface (right) than our base method (left).

Figure 13. Reconstructed meshes and corresponding error maps for a scene from the DTU dataset. Discarded points are colored in blue, while evaluated points are shown in grey for low error and red for high error. Our method produces closed meshes, whereas PGSR reconstructs only a front-facing surface. Notably, points reconstructed by our method near the mesh boundaries exhibit significant error contributions. This problem is largely resolved by our filtering proecdure.

Method	Avg. Peak VRAM (GB)	Max. Peak VRAM (GB)	Avg. Runtime (min)	Chamfer Distance $\downarrow$
PGSR	3.9	5.5	41.4	0.53
MiLO	5.2	8.9	69.6	0.68
ADELE (full)	31.9	33.1	30.3	0.53
ADELE (smaller batch)	21.4	22.5	14	0.56

Appendix

Table 5. Comparison of memory usage, runtime, and reconstruction quality on DTU. Peak VRAM is measured during training; runtime is the average wall-clock training time per scene; Chamfer distance is the mean over all evaluated scenes (lower is better).

Figure 14. Qualitative comparison on the Stanford ORB dataset. For each scene, we show the ground truth image, our rendered image, our predicted mesh normals, and mesh reconstructions from our method, PGSR, and MiLO. Our method produces detailed meshes that faithfully capture object silhouettes and surface+details. PGSR struggles with reflective surfaces, while MiLO tends to produce simplified geometry that misses fine-grained features such as the gnome’s beard and the cactus spines.

	Chamfer Distance $\times$ $2e3\downarrow$
Scene	Gnome	Cactus	Ball	Teapot	Pitcher	Avg
PGSR	0.21	0.08	0.07	0.16	2.10	0.52
MiLO	0.21	0.12	0.11	0.21	0.90	0.31
Ours	0.42	0.05	0.05	0.14	0.99	0.33
	Triangle Count $\downarrow$
Scene	Gnome	Cactus	Ball	Teapot	Pitcher	Avg

Appendix

Table 6. Quantitative comparison on Stanford ORB. We report Chamfer distance (

\downarrow

) scaled by

2e3

as proposed in the official evaluation guidelines, and triangle count of the extracted meshes.

Figure 15. Diffuse-shaded renderings of extracted geometry. Comparison on representative scenes from NeRF Synthetic and BlendedMVS. ADELE produces sharp, realistic renderings that preserve fine appearance detail, whereas PGSR and MILo smooth over high-frequency content as a consequence of their less accurate geometric reconstruction.

		PSNR $\uparrow$ – Stanford ORB
Render	Method	Gnome	Cactus	Ball	Teapot	Pitcher	Avg
Native	PGSR	37.91	37.85	36.91	37.43	31.46	36.31
	MiLo	37.01	37.17	34.80	37.57	32.98	35.91
	Ours	35.24	35.09	37.45	35.85	32.96	35.31
Mesh	PGSR	30.93	32.25	31.04	31.56	27.91	30.74
	MiLo	30.34	31.73	29.38	29.71	29.56	30.14

Appendix

Table 7. Novel-view synthesis under two rendering protocols. Native rendering uses each method’s own renderer (3DGS for PGSR and MiLo, neural-shaded mesh rasterization for ours); Extracted-mesh rendering renders the extracted mesh shaded with a per-vertex diffuse albedo. We report PSNR (

\uparrow

) on Stanford ORB (top) and DTU (bottom).

Figure 16. Full results of our method on the 15 scenes of the DTU dataset used in the evaluation of the main paper.

Figure 17. Effect of depth offset rendering. Training with regular mesh rendering (top) produces both convex and concave surface artefacts across a variety of scenes. Training with depth offset rendering (bottom) largely eliminates them.

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