mlsanityData to 14 Oct 2026

Approximate Differentiable Rendering with Algebraic Surfaces

arXiv 2207.10606 ↗First posted 21 Jul 2022cs.CV cs.AI cs.GRcited by 44

Not on the map. Why?

Abstract (arXiv)

Differentiable renderers provide a direct mathematical link between an object's 3D representation and images of that object. In this work, we develop an approximate differentiable renderer for a compact, interpretable representation, which we call Fuzzy Metaballs. Our approximate renderer focuses on rendering shapes via depth maps and silhouettes. It sacrifices fidelity for utility, producing fast runtimes and high-quality gradient information that can be used to solve vision tasks. Compared to mesh-based differentiable renderers, our method has forward passes that are 5x faster and backwards passes that are 30x faster. The depth maps and silhouette images generated by our method are smooth and defined everywhere. In our evaluation of differentiable renderers for pose estimation, we show that our method is the only one comparable to classic techniques. In shape from silhouette, our method performs well using only gradient descent and a per-pixel loss, without any surrogate losses or regularization. These reconstructions work well even on natural video sequences with segmentation artifacts. Project page: https://leonidk.github.io/fuzzy-metaballs

Key facts. Cited by 44 papers in the map (data through 14 Oct 2026). Builds on 30 of its 90 references that are in the map. First posted on arXiv 21 Jul 2022.

Builds on

30 of 90 references.

References · 30

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2017Mask R-CNNcited by 7,277
  3. 2020RAFT: Recurrent All-Pairs Field Transforms for Optical Flowcited by 2,415
  4. 2020Accelerating 3D Deep Learning with PyTorch3Dcited by 784
  5. 2018Open3D: A Modern Library for 3D Data Processingcited by 721
  6. 2021DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Camerascited by 687
  7. 2021Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstructioncited by 652
  8. 2020Modular Primitives for High-Performance Differentiable Renderingcited by 441
  9. 2017Neural 3D Mesh Renderercited by 437
  10. 2019Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoningcited by 420
  11. 2016The CMA Evolution Strategy: A Tutorialcited by 377
  12. 2020Single-View View Synthesis with Multiplane Imagescited by 263
18 more
  1. 2019Differentiable Surface Splatting for Point-based Geometry Processingcited by 239
  2. 2019Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderercited by 221
  3. 2016Thingi10K: A Dataset of 10,000 3D-Printing Modelscited by 183
  4. 2017MoFA: Model-based Deep Convolutional Face Autoencoder for Unsupervised Monocular Reconstructioncited by 163
  5. 2017Learning Efficient Point Cloud Generation for Dense 3D Object Reconstructioncited by 133
  6. 2018CubeSLAM: Monocular 3D Object SLAMcited by 102
  7. 2018Unsupervised Learning of Shape and Pose with Differentiable Point Cloudscited by 89
  8. 2017Intel RealSense Stereoscopic Depth Camerascited by 83
  9. 2016CMA-ES for Hyperparameter Optimization of Deep Neural Networkscited by 48
  10. 2020End-to-End Learning Local Multi-view Descriptors for 3D Point Cloudscited by 47
  11. 2021Tangent Space Backpropagation for 3D Transformation Groupscited by 40
  12. 2020PointGMM: a Neural GMM Network for Point Cloudscited by 33
  13. 2021Differentiable Surface Rendering via Non-Differentiable Samplingcited by 28
  14. 2022VoGE: A Differentiable Volume Renderer using Gaussian Ellipsoids for Analysis-by-Synthesiscited by 22
  15. 2019Mine Tunnel Exploration using Multiple Quadrupedal Robotscited by 8
  16. 2020GMMLoc: Structure Consistent Visual Localization with Gaussian Mixture Modelscited by 5
  17. 2020MRFMap: Online Probabilistic 3D Mapping using Forward Ray Sensor Modelscited by 4
  18. 2019Direct Fitting of Gaussian Mixture Modelscited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 17; 2024: 16; 2025: 6; 2026: 4.

44 papers.

Sort:

By area:

  1. 20234D Gaussian Splatting for Real-Time Dynamic Scene Renderingcited by 1,157
  2. 20242D Gaussian Splatting for Geometrically Accurate Radiance Fieldscited by 1,076
  3. 2023Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstructioncited by 759
  4. 2023Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesiscited by 737
  5. 2023Gaussian Splatting SLAMcited by 415
  6. 2023SplaTAM: Splat, Track & Map 3D Gaussians for Dense RGB-D SLAMcited by 388
  7. 2023SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenescited by 347
  8. 2024GRM: Large Gaussian Reconstruction Model for Efficient 3D Reconstruction and Generationcited by 301
  9. 2023GS-SLAM: Dense Visual SLAM with 3D Gaussian Splattingcited by 278
  10. 2024Gaussian Opacity Fields: Efficient Adaptive Surface Reconstruction in Unbounded Scenescited by 232
  11. 2023GS-IR: 3D Gaussian Splatting for Inverse Renderingcited by 224
  12. 2024A Hierarchical 3D Gaussian Representation for Real-Time Rendering of Very Large Datasetscited by 216
32 more
  1. 2024MoSca: Dynamic Gaussian Fusion from Casual Videos via 4D Motion Scaffoldscited by 179
  2. 2023HUGS: Human Gaussian Splatscited by 154
  3. 20243D Gaussian Ray Tracing: Fast Tracing of Particle Scenescited by 139
  4. 2024Dynamic Gaussian Marbles for Novel View Synthesis of Casual Monocular Videoscited by 97
  5. 2024Spec-Gaussian: Anisotropic View-Dependent Appearance for 3D Gaussian Splattingcited by 74
  6. 2023Gaussian Shell Maps for Efficient 3D Human Generationcited by 61
  7. 2024PhysAvatar: Learning the Physics of Dressed 3D Avatars from Visual Observationscited by 51
  8. 2023DeformGS: Scene Flow in Highly Deformable Scenes for Deformable Object Manipulationcited by 42
  9. 2022ClimateNeRF: Extreme Weather Synthesis in Neural Radiance Fieldcited by 37
  10. 2023Flexible Techniques for Differentiable Rendering with 3D Gaussianscited by 28
  11. 2023HybridNeRF: Efficient Neural Rendering via Adaptive Volumetric Surfacescited by 28
  12. 2023Gaussian3Diff: 3D Gaussian Diffusion for 3D Full Head Synthesis and Editingcited by 22
  13. 2025Reconstruct, Inpaint, Test-Time Finetune: Dynamic Novel-view Synthesis from Monocular Videoscited by 14
  14. 2024GVKF: Gaussian Voxel Kernel Functions for Highly Efficient Surface Reconstruction in Open Scenescited by 10
  15. 20253DGEER: 3D Gaussian Rendering Made Exact and Efficient for Generic Camerascited by 8
  16. 2023NeRFs: The Search for the Best 3D Representationcited by 7
  17. 2025Articulate That Object Part (ATOP): 3D Part Articulation via Text and Motion Personalizationcited by 7
  18. 2024Monocular Dynamic Gaussian Splatting: Fast, Brittle, and Scene Complexity Rulescited by 6
  19. 2023Incremental Multimodal Surface Mapping via Self-Organizing Gaussian Mixture Modelscited by 5
  20. 20243D Gaussian Splatting for Large-scale Surface Reconstruction from Aerial Imagescited by 5
  21. 2024Distance and Collision Probability Estimation from Gaussian Surface Modelscited by 3
  22. 2024PanoSLAM: Panoptic 3D Scene Reconstruction via Gaussian SLAMcited by 3
  23. 2024Visual SLAM with 3D Gaussian Primitives and Depth Priors Enabling Novel View Synthesiscited by 2
  24. 2026GSO-SLAM: Bidirectionally Coupled Gaussian Splatting and Direct Visual Odometrycited by 2
  25. 2023Discovering Multiple Algorithm Configurationscited by 1
  26. 2024Alpha Invariance: On Inverse Scaling Between Distance and Volume Density in Neural Radiance Fieldscited by 1
  27. 2025RayletDF: Raylet Distance Fields for Generalizable 3D Surface Reconstruction from Point Clouds or Gaussianscited by 1
  28. 2025STAMICS: Splat, Track And Map with Integrated Consistency and Semantics for Dense RGB-D SLAMcited by 0
  29. 2025Extreme Views: 3DGS Filter for Novel View Synthesis from Out-of-Distribution Camera Posescited by 0
  30. 2026Electrostatics-Inspired Surface Reconstruction (EISR): Recovering 3D Shapes as a Superposition of Poisson's PDE Solutionscited by 0
  31. 2026WebSpline: Structure-Informed Splines for Real-Time 3D Gaussians from Monocular Videoscited by 0
  32. 2026CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxationcited by 0