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On the Error Analysis of 3D Gaussian Splatting and an Optimal Projection Strategy

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Computer Vision – ECCV 2024 (ECCV 2024)

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Abstract

3D Gaussian Splatting has garnered extensive attention and application in real-time neural rendering. Concurrently, concerns have been raised about the limitations of this technology in aspects such as point cloud storage, performance, and robustness in sparse viewpoints, leading to various improvements. However, there has been a notable lack of attention to the fundamental problem of projection errors introduced by the local affine approximation inherent in the splatting itself, and the consequential impact of these errors on the quality of photo-realistic rendering. This paper addresses the projection error function of 3D Gaussian Splatting, commencing with the residual error from the first-order Taylor expansion of the projection function. The analysis establishes a correlation between the error and the Gaussian mean position. Subsequently, leveraging function optimization theory, this paper analyzes the function’s minima to provide an optimal projection strategy for Gaussian Splatting referred to Optimal Gaussian Splatting, which can accommodate a variety of camera models. Experimental validation further confirms that this projection methodology reduces artifacts, resulting in a more convincingly realistic rendering.

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Author information

Authors and Affiliations

  1. Nanjing University, Nanjing, China

    Letian Huang, Jiayang Bai, Jie Guo, Yuanqi Li & Yanwen Guo

Authors
  1. Letian Huang
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  2. Jiayang Bai
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  3. Jie Guo
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  4. Yuanqi Li
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  5. Yanwen Guo
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Corresponding author

Correspondence to Jie Guo .

Editor information

Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Aleš Leonardis

  2. University of Trento, Trento, Italy

    Elisa Ricci

  3. Technical University of Darmstadt, Darmstadt, Germany

    Stefan Roth

  4. Princeton University, Princeton, NJ, USA

    Olga Russakovsky

  5. Czech Technical University in Prague, Prague, Czech Republic

    Torsten Sattler

  6. École des Ponts ParisTech, Marne-la-Vallée, France

    Gül Varol

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Huang, L., Bai, J., Guo, J., Li, Y., Guo, Y. (2025). On the Error Analysis of 3D Gaussian Splatting and an Optimal Projection Strategy. In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G. (eds) Computer Vision – ECCV 2024. ECCV 2024. Lecture Notes in Computer Science, vol 15075. Springer, Cham. https://doi.org/10.1007/978-3-031-72643-9_15

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