This study addresses the challenge of accurately segmenting 3D Gaussian Splatting from 2D masks. Conventional methods often rely on iterative gradient descent to assign each Gaussian a unique label, leading to lengthy optimization and sub-optimal solutions. Instead, we propose a straightforward yet globally optimal solver for 3D-GS segmentation. The core insight of our method is that, with a reconstructed 3D-GS scene, the rendering of the 2D masks is essentially a linear function with respect to the labels of each Gaussian. As such, the optimal label assignment can be solved via linear programming in closed form. This solution capitalizes on the alpha blending characteristic of the splatting process for single step optimization. By incorporating the background bias in our objective function, our method shows superior robustness in 3D segmentation against noises. Remarkably, our optimization completes within 30 seconds, about 50× faster than the best existing methods. Extensive experiments demonstrate the efficiency and robustness of our method in segmenting various scenes, and its superior performance in downstream tasks such as object removal and inpainting.
本研究解决了从2D掩码中准确分割3D Gaussian Splatting (3D-GS) 的挑战。传统方法通常依赖迭代的梯度下降算法为每个高斯分配唯一的标签，这导致了冗长的优化过程和次优解。相较之下，我们提出了一种简单且全局最优的3D-GS分割求解器。我们方法的核心洞见在于，对于已重建的3D-GS场景，2D掩码的渲染本质上是与每个高斯的标签相关的线性函数。因此，最优的标签分配可以通过线性规划以闭式形式解决。该方案利用了散点渲染过程中alpha混合的特性，实现了单步优化。通过在目标函数中引入背景偏置，我们的方法在面对噪声时展现出更强的鲁棒性。值得注意的是，我们的优化在30秒内完成，比现有最佳方法快约50倍。广泛的实验表明，我们的方法在分割各种场景中的高效性和鲁棒性，并且在物体移除和修补等下游任务中表现出优越的性能。