In this work we generalize 3D Gaussian splatting (3DGS) to a wider family of physically-based alpha-blending operators. 3DGS has become the standard de-facto for radiance field rendering and reconstruction, given its flexibility and efficiency. At its core, it is based on alpha-blending sorted semitransparent primitives, which in the limit converges to the classic radiative transfer function with exponential transmittance. Inspired by recent research on non-exponential radiative transfer, we generalize the image formation model of 3DGS to non-exponential regimes. Based on this generalization, we use a quadratic transmittance to define sub-linear, linear, and super-linear versions of 3DGS, which exhibit faster-than-exponential decay. We demonstrate that these new non-exponential variants achieve similar quality than the original 3DGS but significantly reduce the number of overdraws, which result on speed-ups of up to $4\times$ in complex real-world captures, on a ray-tracing-based renderer.

翻译：本研究将三维高斯溅射（3DGS）推广至更广泛的基于物理的alpha混合算子族。凭借其灵活性与高效性，3DGS已成为辐射场渲染与重建领域事实上的标准方法。其核心在于对排序后的半透明基元进行alpha混合，在极限情况下收敛于具有指数透射率的经典辐射传输函数。受近期非指数辐射传输研究的启发，我们将3DGS的图像形成模型推广至非指数体系。基于该推广框架，我们采用二次透射率定义出具有亚线性、线性及超线性特性的3DGS变体，这些变体展现出超越指数衰减的加速衰减特性。实验表明，这些新型非指数变体在保持与原始3DGS相近质量的同时，显著减少了过度绘制现象，在基于光线追踪的渲染器中，对复杂现实场景的捕获实现了高达$4\times$的加速效果。