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

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.