3D Gaussian Splatting as Markov Chain Monte Carlo (2404.09591v3)

Abstract: 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) updates 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 initialization.

• The paper introduces a novel MCMC framework for 3D Gaussian Splatting that replaces heuristic Gaussian placement with stochastic Langevin dynamics.
• It leverages an L1 regularizer to reduce the number of Gaussians while maintaining high rendering fidelity and improving scene generalization.
• The study demonstrates enhanced efficiency and quality in neural rendering by enabling robust random initialization and broader applicability in real-world scenes.

Rethinking 3D Gaussian Splatting with MCMC for Neural Rendering

Introduction

3D Gaussian Splatting (3DGS) emerged as an efficient alternative to Neural Radiance Fields (NeRF), significantly reducing the rendering time while producing high-quality images. Despite its advantages, the reliance on heuristically engineered strategies for placing Gaussians—specifically cloning, splitting, and pruning based on adaptive density control—presents limitations in generalization and efficiency. Moreover, a dependence on a favorable initial point cloud poses additional constraints on the applicability of 3DGS to real-world scenes. Addressing these challenges, this work introduces a novel framework that conceptualizes 3D Gaussians as samples drawn from an underlying probability distribution of the scene, utilizing Stochastic Langevin Gradient Dynamics (SGLD) for updates, thereby obviating the need for heuristics in Gaussian placement.

3D Gaussian Splatting and Its Limitations

The initial attraction to 3DGS stems from its speed and the quality of renderings it can produce, attributed to its approach of representing scenes as collections of 3D Gaussians. However, the prevalent strategies for Gaussian management entail a laborious process of manual tuning and do not guarantee optimal resource utilization or generalization across different scenes. Specifically, these strategies often fail in novel environments, demanding an existing high-quality point cloud for satisfactory performance.

MCMC-Based Reformulation for Improved Robustness and Quality

The paper proposes viewing the scene representation as Markov Chain Monte Carlo (MCMC) samples from a scene’s distribution, likening the 3D Gaussian updates to steps in Stochastic Gradient Langevin Dynamics (SGLD). This perspective allows for the natural exploration of scene landscapes without the heuristics previously used for managing Gaussian placements. Key to this approach is the addition of Gaussians as observing more of the recently visited locations within this probabilistic framework, simplifying the process of 3DGS while enhancing the rendering quality.

To address efficiency concerns, an L1-regularizer is introduced, encouraging the use of fewer Gaussians without sacrificing rendering fidelity. This regularization strategy, coupled with the MCMC-based formulation, significantly improves the model's ability to initialize from a broader range of starting points, including random initialization, thereby increasing its robustness and applicability.

Implications and Future Directions

The shift towards a stochastic sampling method for Gaussian placement in neural rendering introduces several advantages over traditional heuristic-based strategies. By eliminating the reliance on specific initialization procedures and heuristic adjustments, this approach simplifies the 3DGS pipeline and enhances its applicability to diverse scenes, including those where previous methods struggled. Moreover, the inclusion of L1 regularization promotes computational efficiency, potentially making high-quality neural rendering more accessible.

This work lays the groundwork for further exploration into probabilistic formulations of scene representations in neural rendering. Future research could delve into the optimization of sampling strategies and regularization techniques, further enhancing the efficiency and quality of rendered images. Additionally, investigating the applicability of similar MCMC-based approaches to other aspects of neural rendering and scene representation could yield interesting insights and advancements in the field.

Conclusion

In summary, this paper presents a novel reinterpretation of 3D Gaussian Splatting within a Markov Chain Monte Carlo framework, utilizing Stochastic Langevin Gradient Descent for Gaussian updates. This approach not only eliminates the need for heuristic-based strategies in Gaussian placement but also shows significant improvements in rendering quality and robustness to initialization. The incorporation of L1 regularization further underscores the method's efficiency, heralding a promising direction for research in neural rendering and scene representation.