3DGS-LM：利用Levenberg-Marquardt算法加速高斯点插值优化

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

September 19, 2024

作者: Lukas Höllein, Aljaž Božič, Michael Zollhöfer, Matthias Nießner

cs.AI

摘要

我们提出了3DGS-LM，这是一种新方法，通过将其ADAM优化器替换为定制的Levenberg-Marquardt（LM）来加速3D高斯飞溅（3DGS）的重建。现有方法通过减少高斯数量或改进可微光栅化器的实现来减少优化时间。然而，它们仍然依赖于ADAM优化器来拟合场景中数千次迭代的高斯参数，这可能需要长达一小时的时间。为此，我们将优化器更改为与3DGS可微光栅化器同时运行的LM。为了实现高效的GPU并行化，我们提出了一种用于中间梯度的缓存数据结构，使我们能够在自定义CUDA核心中高效计算雅可比-向量乘积。在每次LM迭代中，我们使用这些核心从多个图像子集计算更新方向，并将它们组合成加权平均值。总体而言，我们的方法比原始3DGS快30%，同时获得相同的重建质量。我们的优化方法也不受其他加速3DGS的方法的影响，因此与原始3DGS相比，可以实现更快的加速。

English

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.