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Mathematical Supplement for the $\texttt{gsplat}$ Library

Vickie Ye, Angjoo Kanazawa

TL;DR

The mathematical details of the gsplat library are provided, a modular toolbox for efficient differentiable Gaussian splatting, as proposed by Kerbl et al.

Abstract

This report provides the mathematical details of the gsplat library, a modular toolbox for efficient differentiable Gaussian splatting, as proposed by Kerbl et al. It provides a self-contained reference for the computations involved in the forward and backward passes of differentiable Gaussian splatting. To facilitate practical usage and development, we provide a user friendly Python API that exposes each component of the forward and backward passes in rasterization at github.com/nerfstudio-project/gsplat .

Mathematical Supplement for the $\texttt{gsplat}$ Library

TL;DR

The mathematical details of the gsplat library are provided, a modular toolbox for efficient differentiable Gaussian splatting, as proposed by Kerbl et al.

Abstract

This report provides the mathematical details of the gsplat library, a modular toolbox for efficient differentiable Gaussian splatting, as proposed by Kerbl et al. It provides a self-contained reference for the computations involved in the forward and backward passes of differentiable Gaussian splatting. To facilitate practical usage and development, we provide a user friendly Python API that exposes each component of the forward and backward passes in rasterization at github.com/nerfstudio-project/gsplat .
Paper Structure (10 sections, 38 equations)

This paper contains 10 sections, 38 equations.

Table of Contents

  1. Introduction
  2. Rasterization Forward Pass
  3. Projection of Gaussians
  4. Depth Compositing of Gaussians
  5. Computing Gradients of Gaussians
  6. Depth Compositing Gradients
  7. Projection Gradients
  8. Scale and rotation gradients
  9. Conclusion
  10. Acknowledgements