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<title>3D Gaussian Splatting as Markov Chain Monte Carlo</title>
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3D Gaussian Splatting as Markov Chain Monte Carlo
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<a href="https://shakibakh.github.io/">Shakiba Kheradmand</a
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><sup>1</sup>,</span
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>
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<span class="author-block">
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<a href="http://drebain.com/"> Daniel Rebain</a
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><sup>1</sup>,</span
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<span class="author-block">
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<a href="https://hippogriff.github.io/"> Gopal Sharma</a
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><sup>1</sup>,</span
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<span class="author-block">
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<a href="https://wsunid.github.io/"> Weiwei Sun</a
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><sup>1</sup>,</span
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>
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<br />
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<a href="https://scholar.google.com/citations?user=1iJfq7YAAAAJ&hl=en"> Yang-Che Tseng</a
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><sup>1</sup>,</span
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>
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<a href="http://www.hossamisack.com/">Hossam Isack</a
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><sup>2</sup>,
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</span>
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<span class="author-block">
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<a href="https://abhishekkar.info/">Abhishek Kar</a><sup>2</sup>
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<br />
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<span class="author-block">
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<a href="https://taiya.github.io/">Andrea Tagliasacchi</a
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><sup>3, 4, 5</sup>
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</span>
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<span class="author-block">
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<a href="https://www.cs.ubc.ca/~kmyi/">Kwang Moo Yi</a
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><sup>1</sup>
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<span class="author-block"
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><sup>1</sup>University of British Columbia</span
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>
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<span class="author-block"><sup>2</sup>Google Research</span>
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<span class="author-block"><sup>3</sup>Google DeepMind</span>
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<br />
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<span class="author-block"
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><sup>4</sup>Simon Fraser University</span
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>
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<span class="author-block"
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><sup>5</sup>University of Toronto</span
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>
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</a>
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src="./resources/training_rand_compare/bicycle_both-rand.mp4"
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<br>
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<p class="justified">
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Novel view reconstructions for <strong>(right) our method</strong>
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and <strong>(left) conventional</strong> 3D Gaussian Splatting with
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random initializations. Our method, even with random initialization,
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faithfully reconstructs the scene (e.g.. buildings at the back and
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the ground texture) providing much higher quality renderings.
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</p>
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</div>
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<div class="parent-video-compare-container">
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<hr />
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</div>
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<h1>Abstract</h1>
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<div class="parent-video-compare-container">
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<p class="justified">
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While 3D Gaussian Splatting has recently become popular for neural
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rendering, current methods rely on carefully engineered cloning and
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splitting strategies for placing Gaussians, which can lead to
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poor-quality renderings, and reliance on a good initialization. In
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this work, we rethink the set of 3D Gaussians as a random sample
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drawn from an underlying probability distribution describing the
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physical representation of the scene---in other words, Markov Chain
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Monte Carlo (MCMC) samples. Under this view, we show that the 3D
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Gaussian updates can be converted as Stochastic Gradient Langevin
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Dynamics (SGLD) update by simply introducing noise. We then rewrite
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the densification and pruning strategies in 3D Gaussian Splatting as
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simply a deterministic state transition of MCMC samples, removing
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these heuristics from the framework. To do so, we revise the
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`cloning' of Gaussians into a relocalization scheme that
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approximately preserves sample probability. To encourage efficient
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use of Gaussians, we introduce a regularizer that promotes the
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removal of unused Gaussians. On various standard evaluation scenes,
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we show that our method provides improved rendering quality, easy
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control over the number of Gaussians, and robustness to
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initialization.
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</p>
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</div>
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<div class="parent-video-compare-container">
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<hr />
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</div>
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<h1>More Results</h1>
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<div class="parent-video-compare-container">
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<table class="tbl_video" style="width:100%;"">
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<td colspan="4" style="background-color: #d1c4ce; font-size: 20px">
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'10' sequence from OMMO dataset
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</td>
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</tr>
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<tr>
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<td width="50%" style="font-size: 18px">3DGS-Random</td>
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<td width="50%" style="font-size: 18px">3DGS</td>
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</video>
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<td width="50%" style="font-size: 18px">Ours-Random</td>
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<td width="50%" style="font-size: 18px">Ours</td>
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<table class="tbl_video" style="width:100%;"">
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<td colspan="4" style="background-color: #d1c4ce; font-size: 20px">
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'Stump' sequence from the MipNeRF360 dataset (pay attention to the
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details between the leaves)
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</td>
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</tr>
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<tr>
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<td width="50%" style="font-size: 18px">3DGS-Random</td>
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<td width="50%" style="font-size: 18px">3DGS</td>
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<td colspan="2">
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<video
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id="00"
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width="95%"
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preload="auto"
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<source src="resources/stump/stump.mp4" type="video/mp4" />
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</video>
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<tr>
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<td width="50%" style="font-size: 18px">Ours-Random</td>
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<td width="50%" style="font-size: 18px">Ours</td>
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