# CF-Splat: Closed-Form Triangle Splatting with Mesh Priors

arXiv: https://arxiv.org/abs/2610.22108 · HTML: https://mlsanity.com/paper/2610.22108/

## Key facts

- No citing papers in the map yet (data through 19 Oct 2026).
- Placed in 3D Gaussian splatting methods, one of 15 directions in 3D reconstruction and neural rendering.
- Builds on 30 of its 45 references that are in the map.
- First posted on arXiv 15 Oct 2026.

## Placed in

- 3D reconstruction and neural rendering / [3D Gaussian splatting methods](https://mlsanity.com/recon3d/3d-gaussian-splatting-methods/)

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [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)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [OmniObject3D: Large-Vocabulary 3D Object Dataset for Realistic Perception, Reconstruction and Generation](https://mlsanity.com/paper/2301.07525/) (2023)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [PGSR: Planar-based Gaussian Splatting for Efficient and High-Fidelity Surface Reconstruction](https://mlsanity.com/paper/2406.06521/) (2024)
- [UniSim: A Neural Closed-Loop Sensor Simulator](https://mlsanity.com/paper/2308.01898/) (2023)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [Voxblox: Incremental 3D Euclidean Signed Distance Fields for On-Board MAV Planning](https://mlsanity.com/paper/1611.03631/) (2016)
- [Speedy-Splat: Fast 3D Gaussian Splatting with Sparse Pixels and Sparse Primitives](https://mlsanity.com/paper/2412.00578/) (2024)
- [Colonoscopy 3D Video Dataset with Paired Depth from 2D-3D Registration](https://mlsanity.com/paper/2206.08903/) (2022)
- [GaMeS: Mesh-Based Adapting and Modification of Gaussian Splatting](https://mlsanity.com/paper/2402.01459/) (2024)
- [Kimera-Multi: Robust, Distributed, Dense Metric-Semantic SLAM for Multi-Robot Systems](https://mlsanity.com/paper/2106.14386/) (2021)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [3DGS-LM: Faster Gaussian-Splatting Optimization with Levenberg-Marquardt](https://mlsanity.com/paper/2409.12892/) (2024)
- [FastGS: Training 3D Gaussian Splatting in 100 Seconds](https://mlsanity.com/paper/2511.04283/) (2025)
- [The Oxford Spires Dataset: Benchmarking Large-Scale LiDAR-Visual Localisation, Reconstruction and Radiance Field Methods](https://mlsanity.com/paper/2411.10546/) (2024)
- [VILENS: Visual, Inertial, Lidar, and Leg Odometry for All-Terrain Legged Robots](https://mlsanity.com/paper/2107.07243/) (2021)
- [MeshSplatting: Differentiable Rendering with Opaque Meshes](https://mlsanity.com/paper/2512.06818/) (2025)
- [MVGS: Multi-view Regulated Gaussian Splatting for Novel View Synthesis](https://mlsanity.com/paper/2410.02103/) (2024)
- [SLAMesh: Real-time LiDAR Simultaneous Localization and Meshing](https://mlsanity.com/paper/2303.05252/) (2023)
- [Large-Scale LiDAR Consistent Mapping using Hierachical LiDAR Bundle Adjustment](https://mlsanity.com/paper/2209.11939/) (2022)
- [Matrix-free Second-order Optimization of Gaussian Splats with Residual Sampling](https://mlsanity.com/paper/2504.12905/) (2025)
- [CAD-Mesher: A Convenient, Accurate, Dense Mesh-based Mapping Module in SLAM for Dynamic Environments](https://mlsanity.com/paper/2408.05981/) (2024)
- [Opt3DGS: Optimizing 3D Gaussian Splatting with Adaptive Exploration and Curvature-Aware Exploitation](https://mlsanity.com/paper/2511.13571/) (2025)

## Abstract (arXiv)

Splatting-based radiance-field representations have recently gained popularity in robotic perception, enabling high-quality novel-view synthesis (NVS) through explicit scene primitives. However, existing splatting methods typically rely on iterative nonlinear optimization that jointly optimizes millions of coupled primitive parameters, resulting in substantial computation time, peak GPU memory consumption, and susceptibility to local minima. In this paper, we propose CF-Splat, a novel closed-form triangle-splatting framework for efficient scene appearance estimation over a known mesh either pre-existing or provided by upstream mapping or reconstruction pipelines. Our key insight is that, by properly formulating the problem over the given mesh geometry and calibrated cameras, the rendered pixel colors can be expressed linearly with respect to the per-vertex spherical harmonics (SH) coefficients, allowing multi-view scene appearance estimation to be formulated as a global linear least-squares (LLS) problem without the need of iterative nonlinear optimization. To guarantee a well-posed solution under uneven multi-view observation coverage, we introduce adaptive SH regularization that constrains insufficiently supported high-order SH coefficients and yields a unique global minimizer. To ensure the scalability to large-scale scenes, we develop a triangle-structured matrix-free preconditioned conjugate-gradient solver that avoids explicitly constructing the large sparse normal system while producing the same LLS solution. Experiments on diverse real-world datasets demonstrate that CF-Splat achieves competitive or superior NVS quality compared with state-of-the-art splatting methods. While, CF-Splat requires approximately 27.5-378.0 times less computation time and 1.8 times lower peak GPU memory on average than 3DGS across scenes of different scales on a consumer-grade laptop.