Chapter Summary

Chapter Summary

Key Points

• 1.

  3D Gaussian Splatting represents scenes as explicit collections of anisotropic 3D Gaussians, each carrying position, covariance, opacity, and appearance attributes. Differentiable rasterisation enables gradient-based optimisation from observations, achieving training in minutes and rendering at $> 100$ FPS --- orders of magnitude faster than NeRF.

• 2.

  The alpha-compositing formula used by 3DGS is a Riemann-sum discretisation of the NeRF volume rendering integral, establishing a theoretical connection between the two representations.

• 3.

  RF-3DGS adapts 3DGS for radio propagation by replacing optical colour with dB-scale received power, using image-based initialisation (instead of SfM), and optimising a dB-scale loss function to handle the large dynamic range of RF measurements.

• 4.

  RFCanvas fuses visual priors (camera + LiDAR) with few-shot RF measurements, reducing the required RF data by $5\times$ through multi-modal initialisation and tensorial RF fields with spherical harmonics for directional scattering.

• 5.

  RadarSplat and GSpaRC extend 3DGS to automotive radar with FMCW-aware rendering, radar cross-section attributes, and physics-based propagation models. Coherent summation (not incoherent power addition) is essential for correct radar modelling.

• 6.

  The choice between NeRF, 3DGS, and SDF for RF depends on the application: 3DGS excels in speed and interpretability; NeRF handles volumetric diffuse scattering; SDF suits specular-dominated mmWave environments.

• 7.

  Open questions include coherent channel reconstruction (beyond power-only), dynamic RF environments, scalability to large scenes, and theoretical reconstruction guarantees analogous to those available for classical estimators.