通过波段统计约束，提升3D高斯点云的细节还原能力。
KC-3DGS: Kurtosis-Constrained Gaussian Splatting for High-Fidelity View Synthesis
- 引入多尺度小波系数对齐损失，抑制高频信息丢失。
- 结合峰度集中损失，在频域匹配真实图像的重尾分布。
- 适用于低视角数据下的高质量视图合成，尤其适合3DGS初学者。
3D高斯点云（3DGS）通过可微光栅化将场景表示为各向异性高斯集合，实现实时新视角合成。但标准像素空间损失（如L1、SSIM）仅约束整体重建误差，允许优化过程在不同频率尺度间重新分配误差，导致过平滑和结构伪影，尤其在稀疏视角设置下更为明显。本文提出KC-3DGS，基于自然图像统计特性，在小波域引入监督。方法包含三部分：(1) 多尺度小波系数对齐损失，显式惩罚高频细节缺失；(2) 受监督的峰度集中损失，促使渲染图像匹配真实图像的重尾频率统计；(3) 跨带协方差惩罚，促进频率专属性。理论分析表明，像素空间损失在小波重分配下存在一族不可区分的扰动，而联合目标可排除退化解。在MipNeRF360、Tanks&Temples、MVImgNet、DeepBlending和WRIVA-ULTRRA等多个数据集上实验均显示一致的感知质量提升。在具有挑战性的室外数据集WRIVA-ULTRRA上，KC-3DGS使DreamSim提升9.48%，同时改善了PSNR、SSIM和LPIPS。在仅12张训练图像的稀疏视角设置下，于MipNeRF360上最高提升0.5 dB PSNR，且保持感知质量。该方法可无缝集成至现有3DGS流程，作为即插即用的正则化策略。
原文摘要 · Abstract (English)
3D Gaussian Splatting (3DGS) enables real-time novel view synthesis by representing scenes as collections of anisotropic Gaussians optimized via differentiable rasterization. However, standard pixel-space losses (L1, SSIM) constrain only aggregate reconstruction error, permitting the optimization to redistribute error across frequency scales. This leads to oversmoothing and structural artifacts, particularly in sparse-view settings where supervision is limited. We propose KC-3DGS, which augments 3DGS training with wavelet-domain supervision based on natural image statistics. Our method combines three components: (1) a multi-scale wavelet coefficient alignment loss that explicitly penalizes missing high-frequency detail, (2) a supervised kurtosis concentration loss that encourages rendered images to match the heavy-tailed frequency statistics of ground-truth images, and (3) a cross-band covariance penalty that promotes frequency specialization. We provide theoretical analysis showing that pixel-space losses admit a family of indistinguishable perturbations under wavelet redistribution, and that our joint objective excludes degenerate solutions. Experiments across MipNeRF360, Tanks&Temples, MVImgNet, DeepBlending, and WRIVA-ULTRRA demonstrate consistent improvements in perceptual quality. On the challenging WRIVA-ULTRRA outdoor dataset, KC-3DGS achieves a 9.48% improvement in DreamSim while also improving PSNR, SSIM, and LPIPS. In sparse-view settings with only 12 training images, our method improves PSNR by up to 0.5 dB on MipNeRF360 while maintaining perceptual quality. The approach integrates seamlessly into existing 3DGS pipelines as a plug-and-play regularization strategy.
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