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

Johannes Weidenfeller, Shaofei Wang, Philipp Fürnstahl, Siyu Tang

arXiv:2609.06723v1cs.CVcs.GR

TL;DR

Existing multiview reconstruction pipelines often produce meshes through post-training extraction, while direct mesh optimization is limited by fixed resolution and unstable updates. ADELE combines an adaptive Delaunay tetrahedral grid with hybrid volumetric and mesh-based rendering. It significantly outperforms state-of-the-art mesh-based methods across object-centric benchmarks and is competitive with state-of-the-art NeRF/3DGS approaches.

  • Problem

    Post-training mesh extraction can lose fine detail or yield excessively dense meshes, while direct mesh optimization is constrained by fixed-resolution grids and unstable surface updates.

    Source: §1 · p. 2

  • Method

    ADELE combines an optimizable Delaunay tetrahedral grid refined by point pruning and insertion with volumetric rendering for coarse geometry and mesh-based rendering for fine detail.

    Source: §1 · p. 2, §3.2 · p. 4

  • Results

    ADELE significantly outperforms state-of-the-art mesh-based reconstruction methods across DTU, BlendedMVS, NeRF Synthetic, and Stanford ORB, while remaining competitive with state-of-the-art NeRF/3DGS methods.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Direct mesh optimization without auxiliary explicit primitives is a viable alternative for 3D reconstruction, particularly for recovering fine-grained detail and sharp edges.

    Source: §5 · p. 8

    The method uses more memory than competing baselines, remains susceptible to geometric artifacts in highly specular regions, and is restricted to a region of interest in unbounded scenes.

    Source: §5 · p. 8, §4.4 · p. 8

Abstract

from arXiv · show

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.

1 Introduction

Existing reconstruction pipelines often extract meshes after learning radiance fields, risking lost detail or impractically dense meshes, while direct mesh optimization faces fixed-resolution and stability challenges. ADELE combines an adaptive Delaunay grid with hybrid rendering and reports stronger geometric reconstruction than mesh-based methods across several benchmarks.

1 Introduction

  • Radiance-field methods often extract meshes only after training, which can lose fine geometry, produce excessively dense meshes, and reduce rendering fidelity relative to the intermediate representation.These methods commonly use Marching Cubes/Tetrahedra, TSDF fusion, or Poisson reconstruction for extraction.Source: §1 · p. 2
  • Direct mesh optimization links the optimized mesh to rendered output and supports mesh-quality regularization, but fixed-resolution grids constrain detail and training can suffer geometric artifacts and unstable updates.The limitation is especially relevant to regions with complex geometry.Source: §1 · p. 2
  • ADELE uses an optimizable tetrahedral grid periodically rebuilt by Delaunay triangulation, with point pruning and insertion enabling locally adaptive resolution and fine detail.The grid can start from either uniform or random initialization.Source: §1 · p. 2
  • ADELE bootstraps coarse geometry with volumetric rendering, then switches to mesh-based rendering for fine details, using differentiable depth-offset sampling around the rasterized surface.The paper reports that early volumetric rendering stabilizes training but does not produce sharp detail when used in later stages.Source: §1 · p. 2
  • ADELE significantly outperforms state-of-the-art mesh-based reconstruction methods on DTU, BlendedMVS, NeRF Synthetic, and Stanford ORB, while remaining competitive with state-of-the-art NeRF/3DGS methods.The paper also analyzes DTU evaluation bias toward open or incomplete surfaces and filters triangles not visible in at least two input views.Source: §1 · p. 2

2 Related Work

Related work progresses from radiance-field reconstruction toward direct mesh optimization, but extraction quality, resolution limits, and rendering discontinuities remain concerns. ADELE instead optimizes an adaptive Delaunay grid end-to-end with image-space losses and locally adaptive mesh sampling.

2.1 Radiance Fields

2.2 Neural Surface Reconstruction

  • Neural surface methods render SDFs through volumetric density or use 3D Gaussian primitives, yet extraction often remains post-training and can oversmooth high-curvature details.Gaussian Opacity Fields [Yu et al. 2024c] use tetrahedral grids for iso-surface extraction, but retain a separate post-processing step and representation mismatch.Source: §2.2 · p. 3

2.3 Mesh-based Reconstruction

  • Uniform tetrahedral-grid methods remain resolution-limited, while prior adaptive or related mesh approaches have scope gaps; ADELE instead optimizes an adaptive Delaunay grid end-to-end with image-space losses.TetWeave [Binninger et al. 2025] requires ground-truth depth for object-centric reconstruction; Radiant-Foam [Govindarajan et al. 2025] does not extract meshes, and MILo supervises meshes through depth/normal losses rather than image gradients.Source: §2.3 · p. 3

2.4 Mesh-based Rendering

  • Mesh rendering is discontinuous, and existing gradient strategies trade off boundary handling or efficiency; ADELE adds locally adaptive sampling to NVDiffrast, which ablations show stabilizes training and reduces geometric artifacts.Mesh Splatting [Zhang et al. 2026b] softens meshes into blended layers but performs lower on evaluated datasets and struggles with high-frequency detail.Source: §2.4 · p. 3

3 Method

ADELE represents an SDF on an optimizable Delaunay tetrahedral grid with hash-grid features, refining the grid and combining early volumetric supervision with mesh rendering. It also uses per-pixel depth-offset color sampling.

3.1 Geometric Representation

  • The SDF is queried at tetrahedral-grid vertices, and Marching Tetrahedra extracts a watertight mesh from edges whose endpoints have differing SDF signs.The representation combines the tetrahedral grid with a multi-resolution hash grid encoding the SDF.Source: §3.1 · pp. 3–4

3.2 Grid Optimization

  • Grid vertices move as Delaunay connectivity is periodically rebuilt; high-gradient regions guide insertion, while vertices inactive across training views are pruned.New vertices use barycentric coordinates sampled from a uniform Dirichlet distribution; pruning retains neighbors of active vertices as a support region.Source: §3.2 · p. 4

3.3 Hybrid Training

  • Early volumetric rendering bootstraps stable coarse geometry, then training transitions to mesh-based rendering for sharp, fine-grained surface detail.The volumetric supervision weight is gradually reduced over training; using volumetric rendering alone throughout is detrimental to performance.Source: §3.3 · p. 5

3.4 Depth Offset Sampling

  • Per-pixel samples around rasterized depth are blended by opacity contribution; increasing the number of offsets strengthens mesh-gradient alignment with the viewing direction.The sampling-region width is controlled by an optimized parameter σ.Source: §3.4 · p. 5, Figure 4 · p. 5

3.5 Training Losses

  • The model uses an L1 photometric loss, adds mask supervision when masks are available, and includes mesh regularization.Source: Figure 2 · p. 4, §3.5 · p. 5
  • On DTU, ADELE has lower mean Chamfer distance than other mesh-based approaches and performs on par with state-of-the-art radiance-field methods; on BlendedMVS, it has the best mean among mesh methods.Table 1 covers 15 DTU scenes; Table 2 covers 18 BlendedMVS scenes.Source: Table 1 · p. 6, Table 2 · p. 6

4 Experiments

Experiments evaluate ADELE on object-centric datasets, report reconstruction comparisons and component ablations, and examine its performance in unbounded scenes.

4.1 Datasets and Metrics

  • Evaluation covers 15 DTU scenes and 18 low-resolution BlendedMVS scenes using Chamfer distance, and reports PSNR and SSIM for NeRF Synthetic.The datasets include synthetic objects, controlled indoor scans, and in-the-wild captures with intricate shapes.Source: §4.1 · p. 6

4.2 Results

  • ADELE significantly improves over close mesh-based methods on BlendedMVS, outperforms MiLO and performs on par with PGSR on DTU, and has a smaller native-to-mesh PSNR drop than PGSR and MiLO on NeRF Synthetic.On DTU, roof tiles and bird feathers illustrate sharp edges and high-frequency detail with clean mesh quality.Source: §4.2 · pp. 6–7, Figure 5 · p. 7, Table 3 · p. 7

4.3 Ablation Studies

  • Ablations associate volumetric training with stability, adaptive grid refinement with mesh detail, mesh-based rendering with more complete geometry, and offset sampling with fewer scene-specific failures at modest computational cost.Purely mesh-based training is sensitive to initialization, while offset sampling has a small aggregate-metric contribution despite qualitative improvements in affected scenes.Source: Table 4 · p. 7, §4.3 · p. 8

4.4 Large Scale Scenes

  • For unbounded scenes, ADELE uses a coarse SDF from predicted depth for initialization, but models only a bounded central region and leaves background areas unmodeled.The object-centric spherical initialization is insufficient for unbounded scenes.Source: §4.4 · p. 8

5 Conclusion

ADELE's evaluation supports direct mesh optimization as a viable alternative for object-centric reconstruction, particularly for fine details and sharp edges. Memory use, specular-region artifacts, and bounded coverage in unbounded scenes remain limitations.

5 Conclusion

  • Direct mesh optimization without auxiliary explicit primitives is a viable alternative for 3D reconstruction across evaluated object-centric benchmarks, especially for fine details and sharp edges.BlendedMVS comparisons show detailed silhouettes and surface normals, while NeRF Synthetic examples include fine geometry such as leaves and a microphone grille.Source: §5 · p. 8, Figure 7 · p. 9, Figure 9 · p. 10
  • The current pipeline uses more memory than competing baselines, remains susceptible to artifacts in highly specular regions, and is restricted to a region of interest in unbounded scenes.Stronger initialization and improved appearance models are suggested as possible ways to mitigate ambiguities.Source: §5 · p. 8
  • On BlendedMVS, ADELE produces detailed meshes and silhouettes, contrasting with PGSR's overly smooth surfaces and MiLO's high-frequency artifacts.Source: Figure 7 · p. 9
  • On NeRF Synthetic, ADELE recovers fine geometry such as individual leaves and the microphone grille while maintaining clean surface quality.The compared methods exhibit noisy surfaces, silhouette artifacts, or missing geometry.Source: Figure 9 · p. 10

A Implementation Details

The implementation combines adaptive tetrahedral and hash-grid representations with staged volumetric and mesh-based training. Its large-scale variant uses pretrained geometry priors and a decomposed appearance model.

A Implementation Details

  • The scene grid and hash-grid encoder start at the scene center, while the 16-level hash grid encodes both SDF and local appearance at resolutions 32–2048.Training uses a uniformly sampled 250k-point grid, then jointly optimizes volumetric and mesh rendering before switching to mesh-only rendering; densification can reach 1M points.Source: A Implementation Details · p. 13

A.1 Volumetric Rendering Details

  • An occupancy grid updated every 16 iterations skips empty space, with at most 1280 samples per ray and a dynamic batch of 256–8192 rays.Batch size adapts to the preceding iterations’ average volumetric samples per ray to maximize GPU utilization.Source: §A.1 · p. 13
  • Volumetric supervision combines photometric, mask, and Eikonal terms; Eikonal regularization particularly helps in-the-wild scenes with complicated lighting.The volumetric loss is annealed away as the mesh loss rises, fading the volumetric branch after coarse geometry is established.Source: §A.1 · p. 13

A.2 Depth Offset Sampling

  • Depth-offset rendering assumes a locally planar SDF and samples inversely through a sigmoid opacity curve, concentrating samples near the surface for weighted color integration.The camera is assumed to lie outside the surface, so SDF decreases along the ray; sample colors are averaged by their opacity contribution.Source: §A.2 · pp. 13–14, Figure 10 · p. 14

B.1 Initial SDF

  • For large-scale initialization, VGGT camera poses and depth maps yield a TSDF-fused coarse mesh, distilled into a base SDF and combined with a learnable hash-grid residual.The explicit mesh is restricted to a scene-centered region of interest, with a separate environment model for the background.Source: §B.1 · p. 14, Figure 11 · p. 14

B.2 Appearance Model

  • The large-scale appearance model decomposes radiance into view-dependent and reflection-dependent components, blended per sample before volume rendering.Per-image appearance embeddings account for exposure variation in the Tanks and Temples dataset.Source: §B.2 · p. 14

B.3 Implementation Details

The large-scale implementation adapts initialization, optimization schedules, and network settings. A mesh fairness regularizer makes tessellation more even but is omitted from the main evaluation due to an accuracy trade-off.

B.3 Implementation Details

  • Large-scale initialization filters VGGT depth to the most confident 50%, fuses it at 0.02 voxel size, and discretizes the mesh into a 64^3 base SDF.Optimization runs 10,000 iterations with densification from iterations 4,000–8,000 and pruning every 1,000 iterations from iteration 4,000; the ROI side length is 1.5 times median camera distance.Source: §B.3 · pp. 14–15

C Mesh Regularization

  • The fairness regularizer promotes equilateral triangles, but slightly reduces visual and geometric accuracy, so it is excluded from the main method’s evaluation.The regularization strength shown is 0.01.Source: C Mesh Regularization · p. 15

D DTU Evaluation Bias

DTU’s partial ground-truth point clouds can favor open meshes over closed, watertight reconstructions; visibility filtering aligns the compared surface support.

D DTU Evaluation Bias

  • Because DTU ground truth omits backsides, unseen regions of ADELE’s closed meshes can contribute error; visibility filtering removes triangles seen in at most one training view for evaluation only.The filtering aligns prediction support with the partial ground truth and does not improve reconstruction quality.Source: D DTU Evaluation Bias · p. 15

E Memory Analysis

The memory analysis reports peak GPU use, runtime, and reconstruction quality on DTU, including a lower-memory training variant and a triangulation-related memory cost.

E Memory Analysis

  • RadFoam-based Delaunay triangulation accounts for a substantial share of memory; CPU triangulation could reduce GPU use but increase runtime.The authors also report that their reproduced MILo runtimes were substantially longer than the published and originally reported runtimes.Source: E Memory Analysis · p. 15
  • 32 GB peak GPU memory is required by the full method, while a variant uses below 24 GB with slightly reduced reconstruction quality and lower training time.The variant uses one image per batch with gradient accumulation over four optimization steps.Source: E Memory Analysis · p. 15, Table 5 · p. 16

F.1 Stanford ORB

On diffuse-shaded extracted-mesh rendering, ADELE outperforms PGSR and MiLo on Stanford ORB and DTU; on Stanford ORB, all three methods achieve comparable geometric accuracy across most scenes, with some outliers.

F.1 Stanford ORB

  • All three methods achieve comparable geometric accuracy across most Stanford ORB scenes, but PGSR has reflective-pitcher artifacts, MiLo misses the silhouette, and ADELE has artifacts on the rough reflective gnome surface.The evaluation culls triangles invisible from every training view, focusing on image-supervised surfaces without penalizing spurious interior geometry.Source: §F.1 · p. 16

F.2 Novel View Synthesis

  • For Stanford ORB, novel-view PSNR is measured on unseen views, whereas DTU PSNR uses training views because the methods trained on all images.The DTU setup has no common train/test split.Source: §F.2 · p. 16
  • Under diffuse-shaded extracted-mesh rendering, ADELE outperforms PGSR and MiLo on both Stanford ORB and DTU.The authors caution that this protocol discards view-dependent appearance, so lower absolute PSNR does not necessarily indicate worse geometry.Source: §F.2 · p. 16

F.3 Qualitative Results

The supplementary results show qualitative mesh and diffuse-rendering comparisons, full DTU reconstructions, and an ablation in which depth-offset rendering alleviates artifacts from regular mesh rendering.

F.3 Qualitative Results

  • On Stanford ORB, ADELE's detailed meshes capture silhouettes and surface detail, while PGSR struggles with reflective surfaces and MiLo misses fine features such as beard and cactus spines.The comparison includes ground-truth images, ADELE renderings and normals, and reconstructions from ADELE, PGSR, and MiLo.Source: Figure 14 · p. 17
  • Table 7 reports PSNR under native rendering and extracted-mesh diffuse rendering for Stanford ORB and DTU.Native rendering uses each method's own renderer; extracted-mesh rendering uses per-vertex diffuse albedo.Source: Table 7 · p. 17, §F.3 · p. 17
  • Diffuse-shaded mesh renderings show ADELE preserving sharp, realistic high-frequency appearance detail, while PGSR and MiLo smooth over it.The comparison uses representative scenes from NeRF Synthetic and BlendedMVS.Source: Figure 15 · p. 18
  • The supplementary figures present ADELE mesh normals for all 15 evaluated DTU scenes.The full DTU results correspond to the scenes used in the main-paper evaluation.Source: §F.3 · p. 16, Figure 16 · p. 19
  • Depth-offset rendering largely eliminates convex and concave surface artifacts seen with regular mesh rendering across varied scenes.The comparison contrasts regular mesh rendering with depth-offset rendering.Source: §F.3 · p. 16, Figure 17 · p. 20

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