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Beyond Gaussians: Fast and High-Fidelity 3D Splatting with Linear Kernels

Haodong Chen, Runnan Chen, Qiang Qu, Zhaoqing Wang, Tongliang Liu, Xiaoming Chen, Yuk Ying Chung

arXiv:2411.12440v3cs.CV

TL;DR

3DGS still struggles with blur and floating artifacts in high-frequency regions, while kernel design remains underexplored. 3DLS replaces Gaussian kernels with linear kernels and adds distribution and gradient optimizations, achieving state-of-the-art fidelity and accuracy with a 30% FPS increase over 3DGS.

  • Problem

    3DGS has difficulty preserving fine details in high-frequency regions, where Gaussian-kernel softness contributes to blurring and floating artifacts.

  • Method

    3DLS replaces Gaussian kernels with linear kernels and uses Distribution Alignment and Adaptive Gradient Scaling for coverage, compatibility, and stable training.

  • Results

    3DLS achieves state-of-the-art visual fidelity and accuracy across three benchmark datasets and increases FPS by 30% over 3DGS.

  • Takeaways & Limitations

    Kernel design is an important direction for improving fidelity and efficiency in splatting-based rendering, especially for scenes with intricate textures and fine details.

  • Takeaways & Limitations

    Performance gains are stronger on high-frequency scenes; the method is less impactful on smoother datasets and relies on empirically set densification thresholds.

Abstract

from arXiv · show

Recent advancements in 3D Gaussian Splatting (3DGS) have substantially improved novel view synthesis, enabling high-quality reconstruction and real-time rendering. However, blurring artifacts, such as floating primitives and over-reconstruction, remain challenging. Current methods address these issues by refining scene structure, enhancing geometric representations, addressing blur in training images, improving rendering consistency, and optimizing density control, yet the role of kernel design remains underexplored. We identify the soft boundaries of Gaussian ellipsoids as one of the causes of these artifacts, limiting detail capture in high-frequency regions. To bridge this gap, we introduce 3D Linear Splatting (3DLS), which replaces Gaussian kernels with linear kernels to achieve sharper and more precise results, particularly in high-frequency regions. Through evaluations on three datasets, 3DLS demonstrates state-of-the-art fidelity and accuracy, along with a 30% FPS improvement over baseline 3DGS. The implementation will be made publicly available upon acceptance.

1. Introduction

3DLS addresses persistent 3DGS artifacts by replacing Gaussian kernels with linear kernels and adding training optimizations. Across three benchmark datasets, it achieves state-of-the-art fidelity and accuracy while increasing rendering speed by 30%.

  • Gaussian kernels produce soft ellipsoid boundaries that blend neighboring splats, causing floating primitives, over-smoothing, and blurred sharp transitions.
  • 3DLS replaces Gaussian kernels with linear kernels, using bounded support to reduce neighboring-splat interference and capture sharper high-frequency details.The method additionally introduces Distribution Alignment and Adaptive Gradient Scaling for framework compatibility and stable training.
  • Distribution Alignment aligns linear-kernel spread with Gaussian-based methods, while Adaptive Gradient Scaling stabilizes training and balances detail preservation with computational efficiency.
  • 30% FPS improvement over 3DGS accompanies state-of-the-art visual fidelity and accuracy on three benchmark datasets.The reported speed gain has minimal memory overhead and targets real-time applications.

2. Related Work

Prior 3DGS research improves scene structure, geometry, blur handling, rendering consistency, and density control, but kernel design remains comparatively limited. 3DLS addresses this gap by replacing Gaussian kernels with linear ones.

  • 3DGS provides an efficient explicit point-based scene representation, but high-frequency regions can produce artifacts and blurry reconstructions.
  • Existing efforts target scene structure, geometric representation, blurred training images, rendering consistency, and density control.
  • Kernel design remains underexplored, motivating 3DLS's replacement of Gaussian kernels with linear kernels to improve high-frequency detail capture and rendering speed.

3. Methods

3DLS replaces Gaussian kernels with linear attenuation to sharpen high-frequency rendering while preserving the 3DGS pipeline. Distribution Alignment and Adaptive Gradient Scaling address coverage and optimization challenges introduced by the replacement.

  • 3.2. Transition to Linear Kernels: 3DLS replaces Gaussian kernels with linear kernels, reducing blending artifacts and improving high-frequency detail capture.Linear attenuation confines each splat’s influence, producing sharper transitions and clearer reconstructions than smoother Gaussian kernels.
  • 3.2. Transition to Linear Kernels: The linear kernel preserves existing 3DGS accumulation and blending operations, enabling sharper rendering, improved visual fidelity, and faster rendering.
  • 3.3.1. Distribution Alignment (DA): Distribution Alignment scales Mahalanobis distance to broaden the linear kernel’s narrower spread and match Gaussian coverage.The alignment factor preserves coverage while retaining sharper detail capture; Figure 3 illustrates the effect, including λ = 2.5.
  • 3.3.2. Adaptive Gradient Scaling (AGS): Adaptive Gradient Scaling reduces the influence of points farther from the kernel center, stabilizing updates that are otherwise uniform across the linear kernel’s support.AGS uses Mahalanobis distance to modulate gradient magnitudes, mitigating overshooting and oscillations during optimization.

4. Experiments

Across three benchmark datasets, 3DLS consistently improves reconstruction quality over competing methods while increasing rendering speed and maintaining low memory usage. Ablations show that DA improves fidelity, AGS balances detail preservation with efficiency, and the linear kernel reduces primitive requirements.

  • Experimental Setup: Evaluations compare 3DLS with 3DGS, 2DGS, Mip-Splatting, AbsGS, and an anti-aliased 3DLS variant across Mip-NeRF360, Tanks&Temples, and Deep Blending.The experiments include quantitative, qualitative, ablation, and efficiency analyses.
  • Quantitative Comparisons: 3DLS consistently outperforms baselines across diverse datasets and metrics, balancing sharpness, fidelity, and perceptual quality.On Mip-NeRF360 it outperforms 3DGS-based methods in SSIM and PSNR, on Tanks&Temples it leads all three metrics, and on Deep Blending it achieves the best LPIPS.
  • Qualitative Comparisons: Qualitative comparisons show fewer artifacts, sharper transitions, and better preservation of high-frequency details across textured walls, guitar edges, forests, buildings, and door grooves.In the Train background forests, 3DLS is the only compared method reported to reconstruct without noticeable blur.
  • Ablation Study: The linear kernel alone matches baseline 3DGS performance while significantly reducing the number of primitives, producing a more compact representation.This indicates that high-quality reconstruction can be sustained with fewer resources in the ablation scenes.
  • Ablation Study: Distribution Alignment improves performance across all metrics but increases primitive count, whereas Adaptive Gradient Scaling moderates that count while retaining high SSIM and LPIPS and boosting PSNR.AGS optimizes primitive distribution in high-frequency areas to balance detail preservation with computational efficiency.
  • Efficiency Analysis: Over 30% higher forward and backward FPS is achieved with minimal memory overhead, despite higher primitive counts than some methods.The efficiency is attributed to separated linear splats requiring less per-pixel blending than Gaussian splats.

5. Discussion

Kernel choice strongly affects splatting reconstruction, especially in high-frequency regions. The linear kernel is favored because its bounded support and gradual decay preserve detail while reducing artifacts, although the method is less impactful on smooth scenes and remains limited by empirical densification settings and its 3DGS-based architecture.

  • Kernel Design: Linear kernels preserve high-frequency detail across complex patterns more effectively than Gaussian, Laplacian, Cosine, and Quadratic alternatives.The comparison uses stripes, checkerboards, and circles with varying frequencies.
  • Kernel Design: Gaussian and Laplacian long tails blur and overlap in high-frequency regions, while shorter-tailed kernels reduce artifacts but can impose other placement or uniformity trade-offs.The quadratic kernel improves splat uniformity but requires closer splat placement.
  • Kernel Design: The linear kernel’s bounded support and gradual decay confine splat influence, reducing blending artifacts and producing clearer reconstructions.This behavior is presented as the basis for its fidelity and computational advantages.
  • Limitations and Future Work: The method is most effective for datasets with high-frequency details and is less impactful on smoother datasets with continuous surfaces.Future adaptive or hybrid kernels are proposed to broaden performance across scene types.
  • Limitations and Future Work: Densification thresholds are set empirically, and adapting the architecture specifically to linear kernels could further improve performance.The paper identifies systematic threshold optimization and linear-kernel-specific architectural changes as future directions.

6. Conclusion

3DLS improves 3D reconstruction fidelity by replacing Gaussian kernels with linear kernels, achieving strong performance across datasets and faster rendering with minimal memory overhead.

  • 3DLS consistently outperforms existing methods, particularly in scenes with intricate textures and fine details.The approach advances reconstruction fidelity by addressing limitations in traditional 3DGS methods.

Supplementary Material

The supplementary material provides additional technical details, complete per-scene results, and qualitative examples to further demonstrate the proposed approach.

  • The supplementary document adds technical and methodological details, complete per-scene experimental results, and qualitative examples.These materials provide a more comprehensive demonstration of the approach.

A. Implementation Details

The implementation details describe the evaluation setup, composite loss formulation, and densification thresholds used for reproducible experiments.

  • Evaluations use an AMD Ryzen 9 5900X, 32GB RAM, and NVIDIA GeForce RTX 3090 with PyTorch 2.1.0 and CUDA 11.8.The software environment runs on Ubuntu 22.04 LTS.
  • The total loss combines L1, L2, and SSIM terms with weights α = 0.6, β = 0.2, and γ = 0.2.The 6:2:2 weighting balances pixel accuracy, error handling, and structural similarity.
  • Densification thresholds cover gradient, 2D/3D growth, 2D/3D pruning, and opacity pruning for 3DGS-based and 3DLS methods.These thresholds are summarized in Table 4.

B. Generalizing the 3DGS Kernel Function

The generalized kernel formulation models diverse kernels through an attenuation function and applies Distribution Alignment by scaling the Mahalanobis distance.

  • The generalized 3DGS kernel function models different kernel types by choosing different attenuation functions of the Mahalanobis distance.This provides a unified framework for diverse kernel types.
  • Distribution Alignment normalizes the Mahalanobis distance with a scaling factor λ and applies across the listed kernel functions.The method is designed to align kernel spread while preserving a unified formulation.
  • λ = 2.5 aligns Cosine and Linear kernels to the Gaussian distribution, λ = 6 works for Quadratic, and λ = 1 suffices for Laplacian.The scaling produces consistent attenuation behavior across kernels.

C. Per-Scene Experiment Results

The experiments compare 3DLS and its anti-aliased variant with state-of-the-art methods across three datasets using SSIM, PSNR, and LPIPS. Qualitative comparisons show stronger detail preservation and fewer artifacts in complex textures and sharp transitions.

  • C. Per-Scene Experiment Results: Per-scene results compare 3DLS and 3DLS+AA with 3DGS, 2DGS, Mip-Splatting, and AbsGS across Mip-NeRF360, Tanks & Temples, and Deep Blending.Table 5 evaluates SSIM, PSNR, and LPIPS at 7k and 30k iterations.
  • C. Per-Scene Experiment Results: 3DLS improves high-frequency details and intricate textures in the Bicycle, Counter, Flowers, Treehill, Train, and Trucks scenes.These qualitative comparisons are reported in Table 6.
  • C. Per-Scene Experiment Results: 3DLS reduces artifacts and preserves edges around sharp transitions in the Stump, Kitchen, and Dr. Johnson scenes.The reported comparisons specifically highlight these scenes as examples of improved sharp-transition rendering.

E. Additional Kernel Comparisons

Additional kernel comparisons use the PM5544 color pattern to examine behavior across high- and low-frequency regions. Linear kernels perform best on high-frequency details, whereas cosine kernels perform best in uniform color areas.

  • E. Additional Kernel Comparisons: Linear kernels excel at high-frequency details, while cosine kernels perform best in uniform color areas.This comparison is consistent with the analysis in Section 5.1 and suggests kernel-specific behavior across visual regions.
  • E. Additional Kernel Comparisons: The PM5544 pattern combines diverse color blocks with high- and low-frequency regions for comparing kernel behavior.The qualitative comparison evaluates Gaussian, Laplacian, cosine, quadratic, and linear kernels.
  • E. Additional Kernel Comparisons: Kernel performance varies by region type, motivating further exploration of kernel-specific strengths.The reported contrast is between sharper high-frequency detail handling by Linear and stronger uniform-area performance by Cosine.
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