# Gaussian Entropy Fields: Driving Adaptive Sparsity in 3D Gaussian Optimization

arXiv: https://arxiv.org/abs/2512.04542 · HTML: https://mlsanity.com/paper/2512.04542/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 23 of 23)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [MVSNet: Depth Inference for Unstructured Multi-view Stereo](https://mlsanity.com/paper/1804.02505/) (2018)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [Gaussian Opacity Fields: Efficient Adaptive Surface Reconstruction in Unbounded Scenes](https://mlsanity.com/paper/2404.10772/) (2024)
- [PatchmatchNet: Learned Multi-View Patchmatch Stereo](https://mlsanity.com/paper/2012.01411/) (2020)
- [FoV-NeRF: Foveated Neural Radiance Fields for Virtual Reality](https://mlsanity.com/paper/2103.16365/) (2021)
- [Radiative Gaussian Splatting for Efficient X-ray Novel View Synthesis](https://mlsanity.com/paper/2403.04116/) (2024)
- [SparseSat-NeRF: Dense Depth Supervised Neural Radiance Fields for Sparse Satellite Images](https://mlsanity.com/paper/2309.00277/) (2023)
- [Entropy-based Training Methods for Scalable Neural Implicit Sampler](https://mlsanity.com/paper/2306.04952/) (2023)
- [A Critical Analysis of Internal Reliability for Uncertainty Quantification of Dense Image Matching in Multi-view Stereo](https://mlsanity.com/paper/2309.09379/) (2023)

## Built on by (most cited first, 1 of 1)

- [SatSurfGS: Generalizable 2D Gaussian Splatting for Sparse-View Satellite Surface Reconstruction](https://mlsanity.com/paper/2605.07181/) (2026)

## Abstract (arXiv)

3D Gaussian Splatting (3DGS) has emerged as a leading technique for novel view synthesis, demonstrating exceptional rendering efficiency. replaced[]Well-reconstructed surfaces can be characterized by low configurational entropy, where dominant primitives clearly define surface geometry while redundant components are suppressed.The key insight is that well-reconstructed surfaces naturally exhibit low configurational entropy, where dominant primitives clearly define surface geometry while suppressing redundant components. Three complementary technical contributions are introduced: (1) entropy-driven surface modeling via entropy minimization for low configurational entropy in primitive distributions; (2) adaptive spatial regularization using the Surface Neighborhood Redundancy Index (SNRI) and image entropy-guided weighting; (3) multi-scale geometric preservation through competitive cross-scale entropy alignment. Extensive experiments demonstrate that GEF achieves competitive geometric precision on DTU and T&T benchmarks, while delivering superior rendering quality compared to existing methods on Mip-NeRF 360. Notably, superior Chamfer Distance (0.64) on DTU and F1 score (0.44) on T&T are obtained, alongside the best SSIM (0.855) and LPIPS (0.136) among baselines on Mip-NeRF 360, validating the framework's ability to enhance surface reconstruction accuracy without compromising photometric fidelity.