# LEGS: Laplacian-Enhanced Gaussian Splatting with a Nonlinear Weighted Loss

arXiv: https://arxiv.org/abs/2606.07932 · HTML: https://mlsanity.com/paper/2606.07932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [FastGS: Training 3D Gaussian Splatting in 100 Seconds](https://mlsanity.com/paper/2511.04283/) (2025)
- [Side Window Filtering](https://mlsanity.com/paper/1905.07177/) (2019)
- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [Weighted Mean Curvature](https://mlsanity.com/paper/1903.07189/) (2019)
- [Fast and High-Quality Blind Multi-Spectral Image Pansharpening](https://mlsanity.com/paper/2103.09943/) (2021)
- [EdgeGaussians -- 3D Edge Mapping via Gaussian Splatting](https://mlsanity.com/paper/2409.12886/) (2024)
- [EGGS: Edge Guided Gaussian Splatting for Radiance Fields](https://mlsanity.com/paper/2404.09105/) (2024)
- [3DGEER: 3D Gaussian Rendering Made Exact and Efficient for Generic Cameras](https://mlsanity.com/paper/2505.24053/) (2025)
- [Gradient-Direction-Aware Density Control for 3D Gaussian Splatting](https://mlsanity.com/paper/2508.09239/) (2025)
- [Improving Densification in 3D Gaussian Splatting for High-Fidelity Rendering](https://mlsanity.com/paper/2508.12313/) (2025)
- [Opt3DGS: Optimizing 3D Gaussian Splatting with Adaptive Exploration and Curvature-Aware Exploitation](https://mlsanity.com/paper/2511.13571/) (2025)

## Abstract (arXiv)

3D Gaussian Splatting (3DGS) has become an efficient explicit representation for radiance field reconstruction and real-time novel view synthesis. However, its standard photometric loss treats flat and structure-rich regions similarly, which may limit the recovery of sharp contours and fine details. Edge-Guided Gaussian Splatting (EGGS) improves structure awareness through edge-guided weighting, but mainly relies on first-order gradient responses and linear weighting. In this paper, we propose LEGS, a Laplacian-Enhanced Gaussian Splatting method with a nonlinearly weighted loss. LEGS replaces first-order gradient guidance with second-order Laplacian structural guidance and maps the normalized Laplacian response into pixel-wise weights through nonlinear response-to-weight functions. The proposed loss improves structure-aware Gaussian optimization while keeping the original 3DGS rendering pipeline unchanged. Experiments on the full Tanks&Temples and Mip-NeRF360 datasets show that LEGS improves peak signal-to-noise ratio (PSNR) by up to 1.68 dB over 3DGS and up to 0.52 dB over EGGS. Incorporating the proposed second-order nonlinear weighting strategy into FastGS and FasterGS further improves PSNR by up to 1.69 dB, demonstrating its effectiveness as a general loss-level extension for Gaussian Splatting pipelines with potential applications in AR/VR, immersive visualization, and real-time 3D content generation.