$$\mathbf{c}, \sigma = F_{\Theta}(\mathbf{x}, \mathbf{d}),$$ where $\mathbf{c}=(r,g,b)$ is RGB color, $\sigma$ is density, $\mathbf{x}$ is 3D position, $\mathbf{d}$ is the direction.

To explore this issue, I used Kolmogorov-Arnold Networks (KAN) with various basis functions to fit the NeRF equation based on nerfstudio.

• Model Setting -> train_blender.sh

• nerf_synthetic: lego / 30k

• 360_v2: garden / 30k, todo

# create python env
conda create --name nerfstudio -y python=3.8
conda activate nerfstudio
python -m pip install --upgrade pip

# install torch
pip install torch==2.0.1+cu117 torchvision==0.15.2+cu117 --extra-index-url https://download.pytorch.org/whl/cu117
conda install -c "nvidia/label/cuda-11.7.1" cuda-toolkit

# install tinycudann
pip install ninja git+https://github.com/NVlabs/tiny-cuda-nn/#subdirectory=bindings/torch

# install nerfstudio
pip install nerfstudio==0.3.4

# pip install torchmetrics==0.11.4

# Tab command
ns-install-cli

# !!! If you use `ns-process-data`, please install this version opencv
pip install opencv-python==4.3.0.36

############# kan_basis_type #############
# mlp, bspline, grbf, rbf, fourier,
# fcn, fcn_inter, chebyshev, jacobi
# bessel, chebyshev2, finonacci, hermite
# legendre, gegenbauer
bash train_blender.sh

• Universal Approximation Theorem vs. Kolmogorov–Arnold Theorem

• KANeRF, A big thank you for this awesome work!

  @Manual{kanerf,
  title = {Hands-On NeRF with KAN},
  author = {Delin Qu, Qizhi Chen},
  year = {2024},
  url = {https://github.com/Tavish9/KANeRF},
  }

• nerfstudio

   @inproceedings{nerfstudio,
   	title = {Nerfstudio: A Modular Framework for Neural Radiance Field Development},
   	author = {
   		Tancik, Matthew and Weber, Ethan and Ng, Evonne and Li, Ruilong and Yi, Brent
   		and Kerr, Justin and Wang, Terrance and Kristoffersen, Alexander and Austin,
   		Jake and Salahi, Kamyar and Ahuja, Abhik and McAllister, David and Kanazawa,
   		Angjoo
   	},
   	year = 2023,
   	booktitle = {ACM SIGGRAPH 2023 Conference Proceedings},
   	series = {SIGGRAPH '23}
   }