/X-KANeRF

X-KANeRF [KANeRF-benchmarking]: KAN based NeRF with various basis functions like B-Splines, Fourier, Gaussians, Wavelets, Polynomials, etc

Primary LanguagePython

X-KANeRF [KANeRF-benchmarking]: KAN-based NeRF with Various Basis Functions

Is there any basis function can explain the NeRF formula?!

$$\mathbf{c}, \sigma = F_{\Theta}(\mathbf{x}, \mathbf{d}),$$ 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.

The code might be a bit COARSE, any suggestions and criticisms are welcome!

X-KAN Models (Here are various KANs!)

TODO Basis Functions Mathtype Acknowledgement
1 B-Spline $$S_i(x) = a_i + b_i(x - x_i) + c_i(x - x_i)^2 + d_i(x - x_i)^3$$ Efficient-Kan
2 Fourier $$\phi_k(x) = \sin(2\pi kx), \phi_k(x) = \cos(2\pi kx)$$ FourierKAN
3 Gaussian RBF $$\phi(x, c) = e^{-\frac{|x - c|^2}{2\sigma^2}}$$ FastKAN
4 Radial Basis Function $$\phi(x, c) = f(|x - c|)$$ RBFKAN
5 FCN - FCN-KAN
6 FCN-Interpolation - FCN-KAN
7 1st Chebyshev Polynomials $$T_n(x) = \cos(n \cos^{-1}(x))$$ ChebyKAN
8 2nd-Chebyshev Polynomials $$U_n(x) = \frac{\sin((n+1)\cos^{-1}(x))}{\sin(\cos^{-1}(x))}$$ OrthogPolyKANs
9 Jacobi polynomials $$P_n^{(\alpha, \beta)}(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} \left[ (1-x)^{\alpha+n} (1+x)^{\beta+n} \right]$$ JacobiKAN
10 Hermite polynomials $$H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n}(e^{-x^2})$$ OrthogPolyKANs
11 Gegenbauer polynomials $$C_{n+1}^{(\lambda)}(x) = \frac{2(n+\lambda)}{n+1}x C_n^{(\lambda)}(x) - \frac{(n+2\lambda-1)}{n+1}C_{n-1}^{(\lambda)}(x)$$ OrthogPolyKANs
12 Legendre polynomials $$P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n} \left( x^2 - 1 \right)^n$$ OrthogPolyKANs
13 Laguerre polynomials $$L_n(x) = \frac{e^x}{n!} \frac{d^n}{dx^n} \left( x^n e^{-x} \right)$$ OrthogPolyKANs
14 Bessel polynomials $$J_n(x) = \sum_{k=0}^{\infty} \frac{(-1)^k}{k!(n+k)!} \left( \frac{x}{2} \right)^{2k+n}$$ OrthogPolyKANs
15 Fibonacci polynomials $$F_n(x) = xF_{n-1}(x) + F_{n-2}(x), \quad \text{for } n \geq 2.$$ OrthogPolyKANs
16 Lucas polynomials $$L_n(x) = xL_{n-1}(x) + L_{n-2}(x)$$ OrthogPolyKANs
17 Mexican hat wavelet $$\psi(x) = \frac{2}{\sqrt{3a}\pi^{\frac{1}{4}}} \left(1 - \frac{x^2}{a^2}\right) e^{-\frac{x^2}{2a^2}}$$ Wav-KAN
18 Morlet wavelet (Gabor wavelet) $$\psi(t) = \pi^{-\frac{1}{4}} e^{i\omega_0 t} e^{-\frac{t^2}{2}}$$ Wav-KAN
19 Difference of Gaussians(DoG) $$\text{DoG}(x, y) = \frac{1}{\sqrt{2\pi}\sigma_1} e^{-\frac{x^2 + y^2}{2\sigma_1^2}} - \frac{1}{\sqrt{2\pi}\sigma_2} e^{-\frac{x^2 + y^2}{2\sigma_2^2}}$$ Wav-KAN
20 Meyer wavelet $$\psi(x) = \sqrt{\frac{2}{T}} \sum_{k=1}^{N} \left(1 - \left(\frac{k}{N}\right)^2\right) \left[ \cos\left(\frac{2\pi x k}{T}\right) - \frac{\sin(\pi x k / T)}{\pi x k / T}\right]$$ Wav-KAN
21 Shannon wavelet $$\psi(t) = \frac{\sin(\pi t) - \sin\left(\frac{\pi t}{2}\right)}{\pi t}$$ Wav-KAN
22 Bump wavelet $$\psi(t) = e^{-\frac{1}{1 - t^2}}$$ Wav-KAN
More and More!!! - - -

Performance Comparision on RTX-3090

Model hidden_dim hidden_dim_color num_layers num_layers_color geo_feat_dim appearance_embed_dim
Nefacto-MLP-A 32 32 2 2 7 8
Nefacto-MLP-B 8 8 8 8 7 8
Others 8 8 1 1 7 8
  • nerf_synthetic: lego / 30k

Note that the current Train Rays/Sec and Train Time(ETA Time) are not accurate, they are the values ​​when the number of iterations reaches 100.

Model Layer Params $\downarrow$ Train Rays/Sec $\uparrow$ Train Time $\downarrow$ FPS $\uparrow$ PSNR $\uparrow$ SSIM $\uparrow$ LPIPS $\downarrow$
Nerfacto-MLP-A 9902 ~170K ~14m 0.71 32.53 0.968 0.0167
Nerfacto-MLP-B 3382 ~165K ~14m 0.75 27.11 0.915 0.0621
Nerfacto-MLP 1118 ~190K ~13m 0.99 28.60 0.952 0.0346
BSplines-KAN 8092 ~37K ~54 m 0.19 32.33 0.965 0.0174
GRBF-KAN 3748 ~115K ~19 m 0.50 32.39 0.967 0.0172
RBF-KAN 3512 ~140K ~15m 0.71 32.57 0.966 0.0177
Fourier-KAN 5222 ~80K ~25 m 0.42 31.72 0.956 0.0241
FCN-KAN(Iters: 4k) 5184 ~4K ~90m 0.02 29.67 0.938 0.0401
FCN-Interpolation-KAN 6912 ~52K ~40m 0.21 32.67 0.965 0.0187
1st Chebyshev-KAN 4396 ~53K ~40m 0.34 28.56 0.924 0.0523
1st Chebyshev-KAN(faster) 4426 ~86K ~23m 0.45 28.54 0.924 0.0514
Jacobi-KAN 3532 ~72K ~30m 0.37 27.88 0.915 0.0553
Bessel-KAN 3532 ~76K ~28m 0.33 25.79 0.878 0.1156
2nd Chebyshev-KAN 4396 ~55K ~39m 0.33 28.53 0.924 0.0500
Fibonacci-KAN 4396 ~65K ~32m 0.34 28.30 0.922 0.0521
Gegenbauer-KAN 4396 ~53K ~40m 0.32 28.39 0.922 0.0514
Hermite-KAN 4396 ~55K ~38m 0.37 27.58 0.913 0.0591
Legendre-KAN 4396 ~55K ~38m 0.33 26.64 0.893 0.0986
Lucas-KAN 3532 ~75K ~28m 0.42 27.95 0.916 0.0550
Laguerre-KAN 3532 ~74K ~28m 0.39 27.39 0.912 0.0593
MexicanHat-KAN 3614 ~66K ~32m 0.35 31.23 0.961 0.0221
Morlet-KAN 3614 ~67K ~31m 0.38 13.06 0.686 0.2583
DoG-KAN 3614 ~75K ~28m 0.41 32.59 0.966 0.0174
Meyer-KAN 3614 ~36K ~55m 0.17 11.91 0.728 0.2991
Shannon-KAN 3614 ~73K ~28m 0.49 9.15 0.738 0.4434
Bump-KAN 3614 ~70K ~28m 0.33 1.79 0.147 0.9072

Nerfstudio Installation

# 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

Run

# Train
############# kan_basis_type #############
# mlp, bspline, grbf, rbf, fourier,
# fcn, fcn_inter, chebyshev, jacobi
# bessel, chebyshev2, finonacci, hermite
# legendre, gegenbauer, lucas, laguerre
# mexican_hat, morlet, dog, meyer, shannon, bump
bash train_blender.sh [kan_basis_type]

# eval
bash run_eval.sh [exp_path]

# render RGB & Depth
bash run_render.sh [exp_path]

Docs

Citation

If you use this benchmark in your research, please cite this project.

@misc{xkanerf,
	title={X-KANeRF: KAN-based NeRF with Various Basis Functions},
	author={Linfei Li},
	howpublished = {\url{https://github.com/lif314/X-KANeRF}},
	year={2024}
}

Acknowledgement

  • 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}
 }