# VoGE: A Differentiable Volume Renderer using Gaussian Ellipsoids for Analysis-by-Synthesis

arXiv: https://arxiv.org/abs/2205.15401 · HTML: https://mlsanity.com/paper/2205.15401/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Differentiable Surface Splatting for Point-based Geometry Processing](https://mlsanity.com/paper/1906.04173/) (2019)
- [NeRS: Neural Reflectance Surfaces for Sparse-view 3D Reconstruction in the Wild](https://mlsanity.com/paper/2110.07604/) (2021)
- [RePOSE: Fast 6D Object Pose Refinement via Deep Texture Rendering](https://mlsanity.com/paper/2104.00633/) (2021)
- [Robust Object Detection under Occlusion with Context-Aware CompositionalNets](https://mlsanity.com/paper/2005.11643/) (2020)
- [StarMap for Category-Agnostic Keypoint and Viewpoint Estimation](https://mlsanity.com/paper/1803.09331/) (2018)
- [NeMo: Neural Mesh Models of Contrastive Features for Robust 3D Pose Estimation](https://mlsanity.com/paper/2101.12378/) (2021)
- [View Generalization for Single Image Textured 3D Models](https://mlsanity.com/paper/2106.06533/) (2021)
- [Material Editing Using a Physically Based Rendering Network](https://mlsanity.com/paper/1708.00106/) (2017)
- [Neural View Synthesis and Matching for Semi-Supervised Few-Shot Learning of 3D Pose](https://mlsanity.com/paper/2110.14213/) (2021)

## Built on by (most cited first, 22 of 22)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [SplaTAM: Splat, Track & Map 3D Gaussians for Dense RGB-D SLAM](https://mlsanity.com/paper/2312.02126/) (2023)
- [GS-SLAM: Dense Visual SLAM with 3D Gaussian Splatting](https://mlsanity.com/paper/2311.11700/) (2023)
- [GauHuman: Articulated Gaussian Splatting from Monocular Human Videos](https://mlsanity.com/paper/2312.02973/) (2023)
- [EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis](https://mlsanity.com/paper/2410.01804/) (2024)
- [Approximate Differentiable Rendering with Algebraic Surfaces](https://mlsanity.com/paper/2207.10606/) (2022)
- [Flexible Techniques for Differentiable Rendering with 3D Gaussians](https://mlsanity.com/paper/2308.14737/) (2023)
- [HybridNeRF: Efficient Neural Rendering via Adaptive Volumetric Surfaces](https://mlsanity.com/paper/2312.03160/) (2023)
- [6DGS: 6D Pose Estimation from a Single Image and a 3D Gaussian Splatting Model](https://mlsanity.com/paper/2407.15484/) (2024)
- [Benchmarking Robustness in Neural Radiance Fields](https://mlsanity.com/paper/2301.04075/) (2023)
- [NOVUM: Neural Object Volumes for Robust Object Classification](https://mlsanity.com/paper/2305.14668/) (2023)
- [iNeMo: Incremental Neural Mesh Models for Robust Class-Incremental Learning](https://mlsanity.com/paper/2407.09271/) (2024)
- [Common3D: Self-Supervised Learning of 3D Morphable Models for Common Objects in Neural Feature Space](https://mlsanity.com/paper/2504.21749/) (2025)
- [GlanceVAD: Exploring Glance Supervision for Label-efficient Video Anomaly Detection](https://mlsanity.com/paper/2403.06154/) (2024)
- [Unsupervised Learning of Category-Level 3D Pose from Object-Centric Videos](https://mlsanity.com/paper/2407.04384/) (2024)
- [PanoSLAM: Panoptic 3D Scene Reconstruction via Gaussian SLAM](https://mlsanity.com/paper/2501.00352/) (2024)
- [SplatPose: Geometry-Aware 6-DoF Pose Estimation from Single RGB Image via 3D Gaussian Splatting](https://mlsanity.com/paper/2503.05174/) (2025)
- [HISR: Hybrid Implicit Surface Representation for Photorealistic 3D Human Reconstruction](https://mlsanity.com/paper/2312.17192/) (2023)
- [Learning a Category-level Object Pose Estimator without Pose Annotations](https://mlsanity.com/paper/2404.05626/) (2024)
- [GRMM: Real-Time High-Fidelity Gaussian Morphable Head Model with Learned Residuals](https://mlsanity.com/paper/2509.02141/) (2025)

## Abstract (arXiv)

The Gaussian reconstruction kernels have been proposed by Westover (1990) and studied by the computer graphics community back in the 90s, which gives an alternative representation of object 3D geometry from meshes and point clouds. On the other hand, current state-of-the-art (SoTA) differentiable renderers, Liu et al. (2019), use rasterization to collect triangles or points on each image pixel and blend them based on the viewing distance. In this paper, we propose VoGE, which utilizes the volumetric Gaussian reconstruction kernels as geometric primitives. The VoGE rendering pipeline uses ray tracing to capture the nearest primitives and blends them as mixtures based on their volume density distributions along the rays. To efficiently render via VoGE, we propose an approximate closeform solution for the volume density aggregation and a coarse-to-fine rendering strategy. Finally, we provide a CUDA implementation of VoGE, which enables real-time level rendering with a competitive rendering speed in comparison to PyTorch3D. Quantitative and qualitative experiment results show VoGE outperforms SoTA counterparts when applied to various vision tasks, e.g., object pose estimation, shape/texture fitting, and occlusion reasoning. The VoGE library and demos are available at: https://github.com/Angtian/VoGE.