Novel view synthesis and 3D reconstruction have advanced rapidly with radiance fields and splatting, yet their memory and computational demands limit their use in resource-constrained settings. We introduce Hexels: novel planar hexagonal surface elements with a first-order spatial color field for efficient 3D scene and 2D image representation. Hexels exploit locally planar regions with smoothly varying appearance using fewer, larger primitives. Their hexagonal support provides an area- and boundary-efficient domain, while the local color field captures appearance variation within each primitive. Across 34 scenes, Hexels improve PSNR over memory-matched 2DGS by 4.53-7.38 dB across datasets while requiring lower training VRAM. We further ablate Hexels by showing that per primitive, Hexels outperform 2DGS by upto 4.74 dB while using lower training VRAM and having 2.31 times faster FPS. Even in unconstrained settings, Hexels offers complementary quality-memory trade-offs. For efficient 3D surface reconstruction, Hexels reduce error by 28.9% compared with memory-matched 2DGS across 15 DTU scans. On 6 Tanks and Temples surface scenes, Hexels achieves the highest mean F1 among compared methods (34.38%, versus 31.72% for 2DGS). We further also show that Hexels, as a general primitive, improves 2D image representation over Image-GS. Hexels push the Pareto frontier on the quality-efficiency trade-off of surface-aligned primitives.
Figures & tables
Figure 1: A Hexel is a planar patch with a soft hexagonal boundary; together, Hexels approximate a 3D surface (left). Its center \bp , orthogonal unit tangents \btu,\btv , and scales su,sv determine its position, orientation, and size (center). Color varies linearly from \bc0 at the center, with RGB gradients \bgu,\bgv along local coordinates u,v . K (spatial weight) controls the patch’s influence: increasing sharpness β sharpens the boundary (right). The tileable hexagonal support and local linear color field jointly exploit structure in scene geometry and appearance, allowing each Hexel to represent larger coherent regions while retaining a controllably sharp boundary.
Figure 2: 2D reconstruction on the Image-GS benchmark. Two 2048×2048 examples from the ImageGS dataset with 10K final primitives per method. Hexels preserves finer boundaries and structure, with lower RGB error.
Figure 3: Hexels converge faster. On the Image-GS benchmark, Hexels show faster convergence versus Image-GS while also outperforming it in terms of PSNR and SSIM.
\multirow 3*Method
Tanks and Temples (10)
Mip-NeRF 360 (9)
DTU (15)
Train
VRAM
FPS
PSNR
SSIM
LPIPS
Deploy.
Train
VRAM
FPS
PSNR
SSIM
LPIPS
Deploy.
Train
VRAM
FPS
PSNR
SSIM
LPIPS
Deploy.
min ↓
GiB ↓
↑
dB ↑
↑
VGG ↓
MB ↓
min ↓
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↑
dB ↑
↑
VGG ↓
MB ↓
min ↓
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VGG ↓
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Volumetric primitives
3DGS
\cellcolor tabtealfirst!55!white7.5
2.11
\cellcolor tabtealfirst!55!white581.8
\cellcolor tabtealfirst!55!white22.95
\cellcolor tabtealfirst!55!white0.773
\cellcolor tabtealfirst!55!white0.361
\cellcolor tabtealfirst!55!white45.15
\cellcolor tabtealfirst!55!white9.8
2.79
\cellcolor tabtealfirst!55!white607.2
23.38
0.599
0.527
\cellcolor tabtealfirst!55!white28.45
\cellcolor tabtealfirst!55!white5.1
\cellcolor tabtealfirst!55!white0.64
\cellcolor tabtealfirst!55!white819.6
\cellcolor tabtealfirst!55!white29.29
\cellcolor tabtealfirst!55!white0.893
0.324
8.43
3D Convex
29.2
\cellcolor tabtealfirst!55!white1.60
114.3
22.20
0.758
0.376
46.90
45.7
\cellcolor tabtealfirst!55!white1.90
83.0
\cellcolor tabtealfirst!55!white23.88
\cellcolor tabtealfirst!55!white0.652
\cellcolor tabtealfirst!55!white0.466
30.35
15.0
0.82
213.3
28.24
0.887
\cellcolor tabtealfirst!55!white0.305
\cellcolor tabtealfirst!55!white8.12
Hybrid primitives
Table 3: Matched primitive budgets. At matched primitive-count budgets, Hexels combines high reconstruction quality with low peak training VRAM and compact models.
Figure 4: Qualitative comparisons under matched model-memory and primitive budgets. Top: fixed Hexels V1 on room (Mip-NeRF360) and Francis (Tanks and Temples). Bottom: fixed V3 on Caterpillar (Tanks and Temples) and DTU scan63. Zoomed crops highlight sharper shelf detail, pedestal carvings, radiator slats, and fruit texture achieved by Hexels over baseline methods.
Figure 5: Unconstrained/Native NVS on Mip-NeRF360 and Tanks and Temples. Densified Hexels V3 preserves fine detail, with PSNR gains (in crops) of 4.84 dB and 6.52 dB over the best baseline.
Figure 6: Efficient Surface reconstruction on DTU and Tanks and Temples scenes. Hexels reduces wall holes, surface fragmentation (see Scan 63) and broken surfaces relative to memory-matched 2DGS and other surface splatting baselines.
Figure 7: Direct surface extraction from Hexels .
Figure 8: Shape, color, and overdraw ablation for Hexels. Gaussian and Hexel shapes are paired with constant color or spatial RGB color gradients (V1) under same optimization conditions. Top: flat and smoothly shaded images using 256 primitives; labels give PSNR. Bottom: overdraw (how many primitives contribute to every pixel - blends/pixel) and per-pixel RGB error for the shaded target;
Figure 9: Overdraw Ablation. Reference images and Gaussian/Hexel reconstructions are followed by their overdraw maps, using 4,096 primitives and same optimization setup. Labels below the maps give mean blends/pixel \ie overdraw; The four ablative settings match those in Figure 8 . This visualization shows that the Hexel primitive requires lower overdraw for similar or better visual quality as compared to Gaussians.
Appendix figures & tables7 assets
Supplementary material from the paper’s appendix.
Appendix
Parameter
Learning rate
Center
1.6×10−4
Log tangent scales
5×10−3
Rotation quaternion
10−3
Opacity logit
10−1
Base RGB
10−2
Spatial color gradients
5×10−3
Appendix
Table 7: Initial learning rates for the Hexel V1-V3 models for NVS experiments. Only parameters enabled by a variant are optimized. All rates are halved after 15K, 20K, and 25K iterations.
Figure 10: Surface loss and initialization ablation on DTU scan24. Ground truth and the five fixed-V3 runs of Table 8 (a). Normal consistency reduces facade roughness and holes; MVS with both losses gives the lowest error on this scan.
Figure 11: Appearance, initialization and primitive number ablation in surface reconstruction. Rows show Hexels V1/V2/V3; columns compare SfM/MVS with fixed/densified promotives on DTU scan24, with both surface losses. V3/MVS retains facade openings in the close-up, and its densified variant has the lowest CD on this scan.
Figure 12: Additional surface reconstruction close-ups. The selected views reveal holes in Triangle Splatting’s skull and pedestal surfaces and spurious sheets above the Caterpillar cab in the memory-matched 2DGS reconstructions. Hexels reduces these artifacts.
Figure 13: Additional Mip-NeRF360 comparisons.
Figure 14: Additional DTU comparisons.
Figure 15: Additional Tanks and Temples comparisons.
3D Gaussian Splatting (3DGS) enables real-time novel view synthesis, but existing general-purpose acceleration methods suffer severe rendering quality degradation when extended to more complex, large-scale scenes. To address this issue, we propose EffGS, a more general acceleration framework that improves training and rendering efficiency while maintaining reconstruction quality comparable to or better than vanilla 3DGS across bounded and large-scale scenes. EffGS combines frequency-aware guidance, localized density control, and adaptive primitive scale modulation. First, an importance scoring mechanism combines pixel-wise reconstruction errors with a difference-of-Gaussians mask scheduled over training to provide stage-dependent spatial guidance. Second, localized densification and pruning restricts density modifications to Gaussians with valid projected footprints in the sampled views. Third, learnable per-Gaussian scale modulation adjusts effective primitive extent during optimization while retaining the Compact Box rasterization rule. Extensive experiments on bounded and large-scale scene datasets demonstrate a favorable balance between reconstruction quality, training time, and primitive count. Component ablations and matched-primitive-budget comparisons further support the effectiveness of the framework.
Changbai Li, Shuo Yang, Yichen Yang +2
Beihang University · Nanyang Technological University
Explicit primitive-based radiance fields such as 3D Gaussian Splatting typically model view-dependent appearance using low-order spherical harmonics (SH). Although efficient to evaluate, SH coefficients dominate per-primitive storage and memory traffic, while their band-limited basis restricts angular detail. We present a thorough, end-to-end comparison of SH and recent spherical appearance models and introduce an implicit alternative that decodes compact per-primitive latent codes using a tiny shared MLP. We integrate all models into the same optimized pipeline, fusing their forward and backward passes into a differentiable CUDA rasterizer and provide a portable WebGL viewer for laptop and mobile GPUs. Our evaluation across reconstruction quality, memory use, and optimization and rendering performance shows that recent spherical models offer the strongest overall quality-efficiency trade-off. Our neural representation is the most compact model evaluated and, compared to third-degree SH, reduces the per-primitive appearance footprint from 192 to 28 bytes, accelerates optimization by 1.3×, while improving reconstruction quality. We further analyze how appearance parametrization shapes optimization, identifying differences in recovered geometry and the tendency of expressive models to absorb non-static scene content. Together, our framework and analysis provide practical guidance for replacing SH beyond what image metrics alone can capture.
Florian Hahlbohm, Jorge Condor, Linus Franke +2
TU Braunschweig · Universit`a della Svizzera italiana · University of Würzburg +1
Neural radiance representations in Gaussian Splatting (GS) deliver high-fidelity color detail but impose substantial rendering overhead from network evaluations. We present a learned sparse scene representation based on 2D surfels, which enables baking the neural component into a hardware-accelerated 2D texture atlas and eliminates runtime network inference. Our 2D surfels carry low-frequency geometry and view-dependent appearance, while view-independent, per-primitive high-frequency texture is encoded with a spatial hash grid and converted into the texture atlas. A novel sparsity objective that penalizes per-primitive kernel falloffs achieves a substantially sparser representation than prior methods. With a compute-optimized ray-surfel intersection shader our approach renders roughly 7 to 9× faster than 3DGS on common benchmarks, and over an order of magnitude faster on individual scenes, while surpassing the perceptual quality and speed of the fastest sparsification methods (FastGS and Speedy-Splat) at PSNR parity. A quality-optimized variant matches the perceptual quality of the strongest baseline while still rendering several times faster. Because inference is one texture fetch per fragment, frame rates can be pushed to 2,700--4,400 FPS with no loss in quality when using the GPU hardware rasterizer.
Neel Kelkar, Simon Niedermayr, Kaloian Petkov +2
Technical University of Munich, Siemens-Healthineers, Munich, Germany · Siemens-Healthineers, Erlangen, Germany