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3D Gaussian Splatting as Markov Chain Monte Carlo

3D Gaussian Splatting as Markov Chain Monte Carlo

1University of British Columbia
2Google Research
3Google DeepMind

4Simon Fraser University
5University of Toronto

Novel view reconstructions for (right) our method
and (left) conventional 3D Gaussian Splatting with
random initializations. Our method, even with random initialization,
faithfully reconstructs the scene (e.g.. buildings at the back and
the ground texture) providing much higher quality renderings.

While 3D Gaussian Splatting has recently become popular for neural
rendering, current methods rely on carefully engineered cloning and
splitting strategies for placing Gaussians, which can lead to
poor-quality renderings, and reliance on a good initialization. In
this work, we rethink the set of 3D Gaussians as a random sample
drawn from an underlying probability distribution describing the
physical representation of the scene—in other words, Markov Chain
Monte Carlo (MCMC) samples. Under this view, we show that the 3D
Gaussian updates can be converted as Stochastic Gradient Langevin
Dynamics (SGLD) update by simply introducing noise. We then rewrite
the densification and pruning strategies in 3D Gaussian Splatting as
simply a deterministic state transition of MCMC samples, removing
these heuristics from the framework. To do so, we revise the
`cloning’ of Gaussians into a relocalization scheme that
approximately preserves sample probability. To encourage efficient
use of Gaussians, we introduce a regularizer that promotes the
removal of unused Gaussians. On various standard evaluation scenes,
we show that our method provides improved rendering quality, easy
control over the number of Gaussians, and robustness to

’10’ sequence from OMMO dataset
3DGS-Random 3DGS
Ours-Random Ours
‘Stump’ sequence from the MipNeRF360 dataset (pay attention to the
details between the leaves)
3DGS-Random 3DGS
Ours-Random Ours

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