Integrate Markov Chain Monte Carlo paper improvements

[dedoubleyou1]

https://ubc-vision.github.io/3dgs-mcmc/

This paper introduced a new conceptual model for how to view the process of gaussian splat optimization and then used that to guide several improvements to the original algorithm, leading to superior results while simplifying the various operations and parameters.

In this paper, we reformulated 3D Gaussian Splatting [14] training as Markov Chain Monte Carlo (MCMC) and implement it via Stochastic Gradient Langevin Dynamics (SGLD). By doing so, we show that we can eliminate the need for point-cloud initialization, and avoid heuristic-based densification, pruning and reset. Not only do we show that this strategy generalizes well across various scenes, outperforming the original 3D Gaussian Splatting [14], but for the first time we show that this leads to a 3DGS implementation that beats NeRF backbones on the challenging MipNeRF3360 [2] dataset.

This is a brief summary from the paper of the changes it introduces:

To summarize, our contributions are: • we reveal the link between 3DGS and MCMC sampling, leading to a simpler optimization; • we replace the heuristics in 3D Gaussian Splatting with a principled relocation strategy; • we introduce regularizer to encourage parsimonious use of Gaussians; • we improve robustness to initialization; • we provide higher rendering quality.