AI 中文总结
该研究提出格拉斯曼体点云绘制用于动态场景渲染，其基元为特定高斯分布，运动模型封闭，无需学习变形场和自定义CUDA。在17个HyperNeRF场景训练速度最快，PSNR、MS-SSIM和LPIPS排名第二。
AI 中文摘要
我们引入了格拉斯曼体点云绘制，这是一种动态场景表示，其基元是在时空\(\mathbb{R}^4\)中的3-平面上支持的高斯分布：一般来说，是沿其法线方向均匀平移的空间2-平面。每个基元携带一个单位法线\(n \in \mathbb{S}^3 / \{ \pm 1 \} \cong \mathrm{Gr}(3,4)\)和一个无约束因子\(L \in \mathbb{R}^{4 \times 3}\)，协方差为\(\Sigma_{4D} = (P_n L)(P_n L)^T\)，其中\(P_n = I - n n^T\)。对于一般的\(L\)和\(n \neq \pm e_0\)，以时间为条件在每一帧返回一个秩-2表面元素。圆盘的法线及其沿该法线的速度可从\(n\)中读取；圆盘形状及其中心的切向漂移由\(L\)设置。现有的原生4D高斯点云绘制方法对满秩时空协方差进行切片，因此其每帧基元是一个体积椭球体；由于条件化会使秩恰好降低一个，切片中的秩-2表面元素需要一个秩-3时空协方差，而上述参数化恰好实现了这些。运动模型是封闭形式的，即不学习变形场，也不需要自定义CUDA：经过条件化的圆盘通过其预计算协方差接口为标准三维高斯点云光栅化器提供数据。舒尔分母中的软钳位对静态方向进行正则化，并连续桥接秩-3静态和秩-2动态行为，因此静态和移动基元形成一个单一的连续族。在MonoDyGauBench的17个HyperNeRF场景上，训练速度在所有比较方法中最快（比最强质量基线快4.9到5.6倍），同时在PSNR、MS-SSIM和LPIPS方面排名第二。代码：此https URL
英文摘要
We introduce Grassmannian splatting, a dynamic scene representation whose primitives are Gaussians supported on 3-planes in spacetime $\R^4$: generically, spatial 2-planes in uniform translation along their normals. Each primitive carries a unit normal $n \in \mathbb S^3/\{\pm 1\} \cong \mathrm{Gr}(3,4)$ and an unconstrained factor $L \in \mathbb R^{4 \times 3}$, with covariance \[ Σ_{4\mathrm{D}} = (P_n L)(P_n L)^T, \qquad P_n = I - n n^T. \] For generic $L$ and $n \neq \pm e_0$, conditioning on time returns a rank-2 surfel at every frame. The normal of the disk and its velocity along that normal are read off from $n$; the disk shape and the tangential drift of its center are set by $L$. Existing native 4D Gaussian splatting methods [\it{Yang et. al. 2023,Duan et. al. 2024}] slice full-rank spacetime covariances, so their per-frame primitive is a volumetric ellipsoid; since conditioning lowers rank by exactly one, a rank-2 surfel in the slice requires a rank-3 spacetime covariance, and the parameterization above realizes exactly these. The motion model is closed form, i.e. no deformation field is learned, and no custom CUDA is required: the conditioned disk feeds a standard 3DGS rasterizer through its precomputed-covariance interface. A soft clamp in the Schur denominator regularizes the static orientation and continuously bridges rank-3 static and rank-2 dynamic behavior, so static and moving primitives form a single continuous family. On the 17 HyperNeRF scenes of MonoDyGauBench, training is fastest among all compared methods (4.9 to 5.6 times faster than the strongest quality baselines), while ranking second in PSNR, MS-SSIM, and LPIPS. Code: https://github.com/PaulCelanCoding/grassmannian-splatting
