# Abstract Rendering: Computing All that is Seen in Gaussian Splat Scenes

arXiv: https://arxiv.org/abs/2503.00308 · HTML: https://mlsanity.com/paper/2503.00308/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 14 of 14)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality](https://mlsanity.com/paper/2401.16663/) (2024)
- [Verification of Deep Convolutional Neural Networks Using ImageStars](https://mlsanity.com/paper/2004.05511/) (2020)
- [How NeRFs and 3D Gaussian Splatting are Reshaping SLAM: a Survey](https://mlsanity.com/paper/2402.13255/) (2024)
- [Splatfacto-W: A Nerfstudio Implementation of Gaussian Splatting for Unconstrained Photo Collections](https://mlsanity.com/paper/2407.12306/) (2024)
- [Neural Voxel Renderer: Learning an Accurate and Controllable Rendering Tool](https://mlsanity.com/paper/1912.04591/) (2019)
- [GS-VTON: Controllable 3D Virtual Try-on with Gaussian Splatting](https://mlsanity.com/paper/2410.05259/) (2024)
- [Semantics-Controlled Gaussian Splatting for Outdoor Scene Reconstruction and Rendering in Virtual Reality](https://mlsanity.com/paper/2409.15959/) (2024)

## Abstract (arXiv)

We introduce abstract rendering, a method for computing a set of images by rendering a scene from a continuously varying range of camera positions. The resulting abstract image-which encodes an infinite collection of possible renderings-is represented using constraints on the image matrix, enabling rigorous uncertainty propagation through the rendering process. This capability is particularly valuable for the formal verification of vision-based autonomous systems and other safety-critical applications. Our approach operates on Gaussian splat scenes, an emerging representation in computer vision and robotics. We leverage efficient piecewise linear bound propagation to abstract fundamental rendering operations, while addressing key challenges that arise in matrix inversion and depth sorting-two operations not directly amenable to standard approximations. To handle these, we develop novel linear relational abstractions that maintain precision while ensuring computational efficiency. These abstractions not only power our abstract rendering algorithm but also provide broadly applicable tools for other rendering problems. Our implementation, AbstractSplat, is optimized for scalability, handling up to 750k Gaussians while allowing users to balance memory and runtime through tile and batch-based computation. Compared to the only existing abstract image method for mesh-based scenes, AbstractSplat achieves 2-14x speedups while preserving precision. Our results demonstrate that continuous camera motion, rotations, and scene variations can be rigorously analyzed at scale, making abstract rendering a powerful tool for uncertainty-aware vision applications.