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A New Split Algorithm for 3D Gaussian Splatting (2403.09143v1)

Published 14 Mar 2024 in cs.GR

Abstract: 3D Gaussian splatting models, as a novel explicit 3D representation, have been applied in many domains recently, such as explicit geometric editing and geometry generation. Progress has been rapid. However, due to their mixed scales and cluttered shapes, 3D Gaussian splatting models can produce a blurred or needle-like effect near the surface. At the same time, 3D Gaussian splatting models tend to flatten large untextured regions, yielding a very sparse point cloud. These problems are caused by the non-uniform nature of 3D Gaussian splatting models, so in this paper, we propose a new 3D Gaussian splitting algorithm, which can produce a more uniform and surface-bounded 3D Gaussian splatting model. Our algorithm splits an $N$-dimensional Gaussian into two N-dimensional Gaussians. It ensures consistency of mathematical characteristics and similarity of appearance, allowing resulting 3D Gaussian splatting models to be more uniform and a better fit to the underlying surface, and thus more suitable for explicit editing, point cloud extraction and other tasks. Meanwhile, our 3D Gaussian splitting approach has a very simple closed-form solution, making it readily applicable to any 3D Gaussian model.

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References (35)
  1. TensoRF: Tensorial Radiance Fields. In Computer Vision - ECCV 2022 - 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXXII (Lecture Notes in Computer Science, Vol. 13692), Shai Avidan, Gabriel J. Brostow, Moustapha Cissé, Giovanni Maria Farinella, and Tal Hassner (Eds.). Springer, 333–350. https://doi.org/10.1007/978-3-031-19824-3_20
  2. A moving least square reproducing kernel particle method for unified multiphase continuum simulation. ACM Trans. Graph. 39, 6 (2020), 176:1–176:15. https://doi.org/10.1145/3414685.3417809
  3. GaussianEditor: Swift and Controllable 3D Editing with Gaussian Splatting. CoRR abs/2311.14521 (2023). https://doi.org/10.48550/ARXIV.2311.14521 arXiv:2311.14521
  4. Text-to-3D using Gaussian Splatting. CoRR abs/2309.16585 (2023). https://doi.org/10.48550/ARXIV.2309.16585 arXiv:2309.16585
  5. Normal Estimation for Point Clouds: A Comparison Study for a Voronoi Based Method. In 2nd Symposium on Point Based Graphics, PBG 2005, Stony Brook, NY, USA, June 21-22, 2005, Marc Alexa, Szymon Rusinkiewicz, Mark Pauly, and Matthias Zwicker (Eds.). Eurographics Association, 39–46. https://doi.org/10.2312/SPBG/SPBG05/039-046
  6. GaussianEditor: Editing 3D Gaussians Delicately with Text Instructions. CoRR abs/2311.16037 (2023). https://doi.org/10.48550/ARXIV.2311.16037 arXiv:2311.16037
  7. PCT: Point cloud transformer. Computational Visual Media 7, 2 (2021), 187–199.
  8. Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition. Image Vis. Comput. 20, 13-14 (2002), 1009–1016. https://doi.org/10.1016/S0262-8856(02)00114-2
  9. Denoising Diffusion Probabilistic Models. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, Hugo Larochelle, Marc’Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (Eds.). https://proceedings.neurips.cc/paper/2020/hash/4c5bcfec8584af0d967f1ab10179ca4b-Abstract.html
  10. Photo-SLAM: Real-time Simultaneous Localization and Photorealistic Mapping for Monocular, Stereo, and RGB-D Cameras. CoRR abs/2311.16728 (2023). https://doi.org/10.48550/ARXIV.2311.16728 arXiv:2311.16728
  11. A Style-Based Generator Architecture for Generative Adversarial Networks. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019. Computer Vision Foundation / IEEE, 4401–4410. https://doi.org/10.1109/CVPR.2019.00453
  12. 3D Gaussian Splatting for Real-Time Radiance Field Rendering. ACM Trans. Graph. 42, 4 (2023), 139:1–139:14. https://doi.org/10.1145/3592433
  13. Robust normal estimation for point clouds with sharp features. Comput. Graph. 34, 2 (2010), 94–106. https://doi.org/10.1016/J.CAG.2010.01.004
  14. PointCNN: Convolution On X-Transformed Points. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada, Samy Bengio, Hanna M. Wallach, Hugo Larochelle, Kristen Grauman, Nicolò Cesa-Bianchi, and Roman Garnett (Eds.). 828–838. https://proceedings.neurips.cc/paper/2018/hash/f5f8590cd58a54e94377e6ae2eded4d9-Abstract.html
  15. Charles Loop. 1987. Smooth subdivision surfaces based on triangles. (1987).
  16. DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps. In Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NeurIPS 2022, New Orleans, LA, USA, November 28 - December 9, 2022, Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (Eds.). http://papers.nips.cc/paper_files/paper/2022/hash/260a14acce2a89dad36adc8eefe7c59e-Abstract-Conference.html
  17. Gaussian Splatting SLAM. CoRR abs/2312.06741 (2023). https://doi.org/10.48550/ARXIV.2312.06741 arXiv:2312.06741
  18. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis. In Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part I (Lecture Notes in Computer Science, Vol. 12346), Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm (Eds.). Springer, 405–421. https://doi.org/10.1007/978-3-030-58452-8_24
  19. DreamFusion: Text-to-3D using 2D Diffusion. In The Eleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.net. https://openreview.net/pdf?id=FjNys5c7VyY
  20. PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation. In 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, July 21-26, 2017. IEEE Computer Society, 77–85. https://doi.org/10.1109/CVPR.2017.16
  21. Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis. In Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, Marc’Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan (Eds.). 6087–6101. https://proceedings.neurips.cc/paper/2021/hash/30a237d18c50f563cba4531f1db44acf-Abstract.html
  22. Denoising Diffusion Implicit Models. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net. https://openreview.net/forum?id=St1giarCHLP
  23. Olga Sorkine and Marc Alexa. 2007. As-rigid-as-possible surface modeling. In Proceedings of the Fifth Eurographics Symposium on Geometry Processing, Barcelona, Spain, July 4-6, 2007 (ACM International Conference Proceeding Series, Vol. 257), Alexander G. Belyaev and Michael Garland (Eds.). Eurographics Association, 109–116. https://doi.org/10.2312/SGP/SGP07/109-116
  24. NeRFEditor: Differentiable Style Decomposition for Full 3D Scene Editing. CoRR abs/2212.03848 (2022). https://doi.org/10.48550/ARXIV.2212.03848 arXiv:2212.03848
  25. DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation. CoRR abs/2309.16653 (2023). https://doi.org/10.48550/ARXIV.2309.16653 arXiv:2309.16653
  26. NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction. In Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, Marc’Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan (Eds.). 27171–27183. https://proceedings.neurips.cc/paper/2021/hash/e41e164f7485ec4a28741a2d0ea41c74-Abstract.html
  27. Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 4 (2004), 600–612. https://doi.org/10.1109/TIP.2003.819861
  28. ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation. CoRR abs/2305.16213 (2023). https://doi.org/10.48550/ARXIV.2305.16213 arXiv:2305.16213
  29. 4D Gaussian Splatting for Real-Time Dynamic Scene Rendering. CoRR abs/2310.08528 (2023). https://doi.org/10.48550/ARXIV.2310.08528 arXiv:2310.08528
  30. DE-NeRF: DEcoupled Neural Radiance Fields for View-Consistent Appearance Editing and High-Frequency Environmental Relighting. In ACM SIGGRAPH 2023 Conference Proceedings, SIGGRAPH 2023, Los Angeles, CA, USA, August 6-10, 2023, Erik Brunvand, Alla Sheffer, and Michael Wimmer (Eds.). ACM, 74:1–74:11. https://doi.org/10.1145/3588432.3591483
  31. PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics. CoRR abs/2311.12198 (2023). https://doi.org/10.48550/ARXIV.2311.12198 arXiv:2311.12198
  32. Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field. ACM Trans. Graph. 42, 4 (2023), 111:1–111:15. https://doi.org/10.1145/3592129
  33. 3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models. ACM Trans. Graph. 42, 4 (2023), 92:1–92:16.
  34. The Unreasonable Effectiveness of Deep Features as a Perceptual Metric. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18-22, 2018. Computer Vision Foundation / IEEE Computer Society, 586–595. https://doi.org/10.1109/CVPR.2018.00068
  35. Drivable 3D Gaussian Avatars. CoRR abs/2311.08581 (2023). https://doi.org/10.48550/ARXIV.2311.08581 arXiv:2311.08581
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Authors (6)
  1. Qiyuan Feng (6 papers)
  2. Gengchen Cao (1 paper)
  3. Haoxiang Chen (13 papers)
  4. Tai-Jiang Mu (19 papers)
  5. Shi-Min Hu (42 papers)
  6. Ralph R. Martin (7 papers)
Citations (4)
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Summary

An Overview of "A New Split Algorithm for 3D Gaussian Splatting"

The paper entitled "A New Split Algorithm for 3D Gaussian Splatting" introduces a novel methodology aimed at addressing the intrinsic challenges faced by 3D Gaussian splatting models. This explicit 3D representation has gained traction in recent times due to its applications in geometric editing and scene generation. Despite its potential, it faces significant limitations, predominantly due to scale and structural inhomogeneities that manifest as visual artifacts like blurring and needle-like distortions.

Technical Insights into the Splitting Algorithm

The core contribution of this research is a new algorithm designed to split an NN-dimensional Gaussian into two separate NN-dimensional Gaussians. This division is governed by a set of conservation constraints ensuring mathematical consistency: specifically, the zero-, first-, and second-order moments of the original Gaussian are preserved across the two new Gaussians. The closed-form solution derived for the given problem maintains these constraints effectively, allowing for seamless integration into existing 3D Gaussian models.

The algorithm eliminates the structural and scale inhomogeneities that plague traditional Gaussian splatting models. By producing more uniform Gaussians that are closer fits to the underlying surfaces of 3D objects, this approach enhances the editability and rendering quality of the models. The closed-form solution is especially noteworthy, as it simplifies the application of the splitting procedure, requiring minimal computational overhead and enabling its use across various implementations of 3D Gaussian models.

Empirical Evaluation and Applications

The paper demonstrates the algorithm’s efficacy through various applications, including explicit Gaussian model editing, point cloud densification, and improved 3D Gaussian learning. For instance, in the context of explicit editing, the ability to split objects using 3D planes or remove specific components with minimal distortion or artifacts is a considerable advance over traditional methods. The splitting procedure significantly reduces undesirable effects like needle-like structures and blurring at object boundaries when editing.

Additionally, the integration of the splitting algorithm into 3D Gaussian model training reveals noticeable improvements in rendering quality. The trained models displayed fewer artifacts and exhibited a higher fidelity to the scene geometry with improved Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS) metrics compared to models without the algorithmic enhancement.

In the domain of point cloud extraction, the new splitting algorithm allows for the generation of more uniformly distributed points, filling in gaps typically found in untextured or flat regions, thus enhancing the utility of Gaussian models for downstream tasks such as segmentation or simulation.

Implications and Future Directions

The implications of this research are broad. Practically, the technique can significantly impact the fields of virtual reality, augmented reality, and other domains where real-time 3D model editing and rendering are crucial. Theoretically, this paper lays the groundwork for further exploration into Gaussian operations, including merging processes to optimize model complexity and storage.

Continued advancements may delve into more scalable solutions for merging and decoupling Gaussians, which could further reduce storage needs and computation, opening up possibilities for extensive 3D model applications in large-scale environments.

In conclusion, the paper provides a substantial contribution to the field of 3D model representation and manipulation by enhancing the Gaussian splatting framework, offering a robust solution to its inherent limitations while fostering further research and development opportunities.

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