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

2026-06-05

AI Summary

Standard 3D Gaussian Splatting (3DGS) treats flat and structurally rich regions uniformly during reconstruction, often failing to recover sharp contours and fine details. This work proposes a second-order structure-guided approach based on the Laplacian operator, which—without altering the original rendering pipeline—introduces structure-aware optimization by mapping normalized Laplacian responses to per-pixel loss weights via a nonlinear response-weight function. Departing from conventional first-order gradients and linear weighting schemes, the method significantly enhances detail reconstruction quality. On the Tanks & Temples and Mip-NeRF360 benchmarks, it achieves PSNR gains of up to 1.68 dB over 3DGS and 0.52 dB over EGGS, while also yielding improvements of up to 1.69 dB when integrated into FastGS/FasterGS frameworks.

Abstract

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.

Problem

• 3D Gaussian Splatting
• structure-aware reconstruction
• photometric loss
• edge guidance
• detail recovery

Innovation

• Laplacian guidance
• nonlinear weighting
• Gaussian Splatting
• structure-aware optimization
• second-order derivatives