Feature lifting has emerged as a crucial component in 3D scene understanding, enabling the attachment of rich image feature descriptors (e.g., DINO, CLIP) onto splat-based 3D representations. The core challenge lies in optimally assigning rich general attributes to 3D primitives while addressing the inconsistency issues from multi-view images. We present a unified, kernel- and feature-agnostic formulation of the feature lifting problem as a sparse linear inverse problem, which can be solved efficiently in closed form. Our approach admits a provable upper bound on the global optimal error under convex losses for delivering high quality lifted features. To address inconsistencies and noise in multi-view observations, we introduce two complementary regularization strategies to stabilize the solution and enhance semantic fidelity. Tikhonov Guidance enforces numerical stability through soft diagonal dominance, while Post-Lifting Aggregation filters noisy inputs via feature clustering. Extensive experiments demonstrate that our approach achieves state-of-the-art performance on open-vocabulary 3D segmentation benchmarks, outperforming training-based, grouping-based, and heuristic-forward baselines while producing lifted features in minutes. Our \textbf{code} is available in the \href{https://github.com/saliteta/splat-distiller/tree/main}{\textcolor{blue}{GitHub}}. We provide additional \href{https://splat-distiller.pages.dev/}{\textcolor{blue}{website}} for more visualization, as well as the \href{https://www.youtube.com/watch?v=CH-G5hbvArM}{\textcolor{blue}{video}}.

翻译：特征提升已成为三维场景理解中的关键组成部分，它使得丰富的图像特征描述符（例如DINO、CLIP）能够附着于基于Splat的三维表示之上。其核心挑战在于如何将丰富的通用属性最优地分配给三维基元，同时解决多视角图像带来的不一致性问题。我们提出了一种统一的、与内核及特征无关的特征提升问题表述，将其构建为一个稀疏线性逆问题，该问题可通过闭式解高效求解。我们的方法在凸损失下，为交付高质量提升特征提供了可证明的全局最优误差上界。为了应对多视角观测中的不一致性和噪声，我们引入了两种互补的正则化策略以稳定解并增强语义保真度。Tikhonov引导通过软对角占优来强制数值稳定性，而后提升聚合则通过特征聚类来过滤噪声输入。大量实验表明，我们的方法在开放词汇三维分割基准测试中达到了最先进的性能，优于基于训练、基于分组和启发式前向的基线方法，同时能在数分钟内生成提升特征。我们的**代码**可在\href{https://github.com/saliteta/splat-distiller/tree/main}{\textcolor{blue}{GitHub}}获取。我们还提供了额外的\href{https://splat-distiller.pages.dev/}{\textcolor{blue}{网站}}以获取更多可视化内容，以及\href{https://www.youtube.com/watch?v=CH-G5hbvArM}{\textcolor{blue}{视频}}。