\begin{table}[h]
\centering
\resizebox{0.70\textwidth}{!}{
\begin{tabular}{ll}
\toprule
Symbol & Definition \\
\midrule
$\mathcal{S}=\{\mathcal{G}_i\}_{i=1}^N$ & Set of $N$ Gaussians \\
$\mathbf{x}_i \in \mathbb{R}^3$ & Center position of Gaussian $i$ \\
$\Sigma_i \in \mathbb{R}^{3\times 3}$ & Covariance matrix of Gaussian $i$ \\
$o_i \in [0,1]$ & Opacity of Gaussian $i$ \\
$\mathbf{s}_i \in \mathbb{R}^3$ & Scale parameters \\
$\mathbf{q}_i \in \mathbb{R}^4$ & Rotation (unit quaternion) \\
$\mathbf{k}_i$ & Spherical harmonics (SH) coefficient vector \\
$d_M(i,j)$ & Directed Mahalanobis distance between $i$ and $j$ \\
$\mathcal{N}_k(i)$ & $k$-nearest neighbors of $i$ under $d_M$ \\
$\mathrm{nn}(\mathbf{y})$ & Nearest neighbor in $\mathcal{S}$ to 3D point $\mathbf{y}$ \\
$\mathbf{1}[\cdot]$ & Indicator function (1 if condition holds, else 0) \\
$\mathcal{A}\setminus\mathcal{B}$ & Set difference \\
$\mathcal{D}(\cdot)$ & Morphological dilation operator \\
$\langle \mathbf{a}, \mathbf{b}\rangle$ & Dot product \\
$\mathrm{softmax}_{j\in\mathcal{N}(i)}(\cdot)$ & Softmax over neighbors of $i$ \\
$\mathrm{sg}(\cdot)$ & Stop-gradient operator \\
$\mathrm{clip}(x;a,b)$ & Element-wise clipping of $x$ to $[a,b]$ \\
\bottomrule
\end{tabular}}
\caption{Main notation used throughout the paper.}
\label{tab:notation}
\end{table}