Title: KC-3DGS: Kurtosis-Constrained Gaussian Splatting for High-Fidelity View Synthesis

Abstract:

3D Gaussian Splatting (3DGS) facilitates real-time novel view synthesis by modeling scenes as collections of anisotropic Gaussians, which are optimized through differentiable rasterization. Despite its efficiency, standard pixel-space loss functions, such as L1 and SSIM, only constrain the aggregate reconstruction error. This limitation allows the optimization process to redistribute errors across various frequency scales, often resulting in oversmoothing and structural artifacts, especially in sparse-view scenarios where supervisory signals are scarce.

To address these issues, we introduce KC-3DGS, a method that enhances 3DGS training with wavelet-domain supervision derived from natural image statistics. Our approach incorporates three key components: first, a multi-scale wavelet coefficient alignment loss that explicitly penalizes the absence of high-frequency details; second, a supervised kurtosis concentration loss that ensures rendered images align with the heavy-tailed frequency statistics of ground-truth images; and third, a cross-band covariance penalty that fosters frequency specialization.

Our theoretical analysis demonstrates that while pixel-space losses permit a family of indistinguishable perturbations under wavelet redistribution, our joint objective effectively excludes these degenerate solutions. Empirical evaluations on the MipNeRF360, Tanks&Temples, MVImgNet, DeepBlending, and WRIVA-ULTRRA datasets confirm consistent gains in perceptual quality. Notably, on the challenging outdoor WRIVA-ULTRRA dataset, KC-3DGS yields a 9.48% improvement in DreamSim, alongside enhancements in PSNR, SSIM, and LPIPS. Furthermore, in sparse-view conditions utilizing only 12 training images, our method boosts PSNR by up to 0.5 dB on MipNeRF360 without compromising perceptual fidelity. Designed as a plug-and-play regularization strategy, KC-3DGS integrates seamlessly into existing 3DGS pipelines.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC