Recently, 3D Gaussian Splatting (3DGS) has enabled photorealistic view synthesis at high inference speeds. However, its splatting-based rendering model makes several approximations to the rendering equation, reducing physical accuracy. We show that splatting and its approximations are unnecessary, even within a rasterizer; we instead volumetrically integrate 3D Gaussians directly to compute the transmittance across them analytically. We use this analytic transmittance to derive more physically-accurate alpha values than 3DGS, which can directly be used within their framework. The result is a method that more closely follows the volume rendering equation (similar to ray-tracing) while enjoying the speed benefits of rasterization. Our method represents opaque surfaces with higher accuracy and fewer points than 3DGS. This enables it to outperform 3DGS for view synthesis (measured in SSIM and LPIPS). Being volumetrically consistent also enables our method to work out of the box for tomography. We match the state-of-the-art 3DGS-based tomography method with fewer points. Being volumetrically consistent also enables our method to work out of the box for tomography. We match the state-of-the-art 3DGS-based tomography method with fewer points.
近年来，三维高斯喷溅（3D Gaussian Splatting, 3DGS）在高推理速度下实现了逼真的视图合成。然而，其基于散点的渲染模型对渲染方程作出了一些近似，从而降低了物理精确性。本文表明，即使在光栅化框架中，这种散点及其近似也是不必要的；我们通过直接对三维高斯进行体积积分，解析地计算穿透率（transmittance），以实现更精确的渲染。 我们利用这一解析穿透率推导出比3DGS更物理精确的alpha值，这些值可以直接在其框架中使用。结果是一种更接近体积渲染方程（类似于光线追踪）的方法，同时享有光栅化的速度优势。我们的方法能够以更少的点表示不透明表面，并具有更高的精确度。这使得我们在视图合成（以SSIM和LPIPS测量）方面超越了3DGS。 此外，由于具有体积一致性，我们的方法可以直接应用于断层成像（tomography），并以更少的点匹配最先进的基于3DGS的断层成像方法。这种体积一致性展示了该方法在逼真渲染和科学应用中的潜力，为物理精确的高效三维渲染和建模提供了新路径。