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3DGS-LM: Faster Gaussian-Splatting Optimization with Levenberg-Marquardt

We present 3DGS-LM, a new method that accelerates the reconstruction of 3D Gaussian Splatting (3DGS) by replacing its ADAM optimizer with a tailored Levenberg-Marquardt (LM). Existing methods reduce the optimization time by decreasing the number of Gaussians or by improving the implementation of the differentiable rasterizer. However, they still rely on the ADAM optimizer to fit Gaussian parameters of a scene in thousands of iterations, which can take up to an hour. To this end, we change the optimizer to LM that runs in conjunction with the 3DGS differentiable rasterizer. For efficient GPU parallization, we propose a caching data structure for intermediate gradients that allows us to efficiently calculate Jacobian-vector products in custom CUDA kernels. In every LM iteration, we calculate update directions from multiple image subsets using these kernels and combine them in a weighted mean. Overall, our method is 30% faster than the original 3DGS while obtaining the same reconstruction quality. Our optimization is also agnostic to other methods that acclerate 3DGS, thus enabling even faster speedups compared to vanilla 3DGS.

我们提出了3DGS-LM,一种通过替换ADAM优化器为定制的Levenberg-Marquardt(LM)方法来加速3D Gaussian Splatting(3DGS)重建的新方法。现有方法通过减少高斯数量或改进可微光栅器的实现来缩短优化时间。然而,这些方法仍然依赖于ADAM优化器来调整场景的高斯参数,需要数千次迭代,可能耗时长达一个小时。为此,我们将优化器更换为与3DGS可微光栅器结合运行的LM。为了实现高效的GPU并行化,我们提出了一种用于缓存中间梯度的数据结构,能够通过自定义的CUDA内核高效计算雅可比矩阵与向量的乘积。在每次LM迭代中,我们使用这些内核从多个图像子集计算更新方向,并通过加权均值将它们结合起来。总体而言,我们的方法比原始3DGS快30%,同时保持相同的重建质量。此外,我们的优化对其他加速3DGS的方法保持兼容,因此相较于基础版3DGS能够实现更快的速度提升。