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Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction

Fast and direct CT reconstruction with 3D Gaussian Splatting.

 

Introduction

This is the official repo of our NeurIPS 2024 paper R²-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction. If you find this repo useful, please give it a star ⭐ and consider citing our paper.

News

• 2024.10.25: Code, data, and models have been released. Welcome to have a try!
• 2024.09.27: Our work has been accepted to NeurIPS 2024.
• 2024.05.31: Our paper is available on arxiv.

1. Installation

We recommend using Conda to set up an environment. We tested the code on Ubuntu 20.04 with an RTX 3090 GPU. For installation issues on other platforms, please refer to Gaussian Splatting.

# Download code
git clone https://github.com/Ruyi-Zha/r2_gaussian.git --recursive

# Install environment
SET DISTUTILS_USE_SDK=1 # Windows only
conda env create --file environment.yml
conda activate r2_gaussian

# Install TIGRE for data generation and initialization
wget https://github.com/CERN/TIGRE/archive/refs/tags/v2.3.zip
unzip v2.3.zip
pip install TIGRE-2.3/Python --no-build-isolation

2. Dataset

You can download datasets (synthetic and real) used in our paper here. We follow NeRF format (folders with meta_data.json). You can find more details of data format and generation process in synthetic dataset and real dataset. Organize data as follows.

└── data
│   ├── synthetic_dataset
│   │   ├── cone_ntrain_50_angle_360
│   │   │   ├── 0_chest_cone  # Case name
│   │   │   │   ├── proj_test  # Projections for 2D rendering evaluation
│   │   │   │   │   └── *.npy
│   │   │   │   ├── proj_train  # Projections for training
│   │   │   │   │   └── *.npy
│   │   │   │   ├── init_*.npy  # initialization point cloud file
│   │   │   │   ├── meta_data.json  # Scanner configuration, projection parameters, etc.
│   │   │   │   ├── vol_gt.npy  # Ground truth volume
│   │   │   └──...
│   │   └──...
│   └── real dataset
│   │   ├── cone_ntrain_50_angle_360
│   │   │   ├── pine  # Case name
│   │   │   └──...
│   │   └──...

You can visually check the scene with python scripts/visualize_scene.py -s <path to data>. Thanks @MrMonk3y for providing code.

We also support NAF format data (*.pickle) used in SAX-NeRF.

We have converted our datasets to NAF format for your convenience. You can find them in here.

3. Running

3.1 Initialization (optional)

We have included initialization files in our dataset. You can skip this step if using our dataset.

For new data, you need to use initialize_pcd.py to generate a *.npy file which stores the point cloud for Gaussian initialization.

python initialize_pcd.py --data <path to data>

Command line arguments for initialize_pcd.py

--data

Path to the source directory containing meta_data.json or *.pickle.

--output

Path to the output *.npy file. <path to data>/<data name>_init.npy by default.

--evaluate

Add this flag to evaluate the 3D PSNR of initial Gaussians. It is used for debugging purpose since it uses the ground truth volume.

--recon_method

Method used for reconstructing initial volume. Now we support fdk (sample from FDK volume) or random (sample randomly). fdk by default.

--n_points

Number of points for initialization. 50000 by default.

--density_thresh

We sample voxels with density higher than the threshold. 0.05 by default.

--density_rescale

We empirically rescale the queried density value to account for occlusion. 0.15 by default.

--random_density_max

Maximum density for random initialization. 1.0 by default.

❗ Initialization is important for most 3DGS-based methods, including ours. We initialize the point clouds by sampling from a noisy volume reconstructed using the FDK algorithm.

Our default settings assume the density ranges from [0, 1]. You may need to adjust the parameters in initialize_pcd.py according to your dataset to achieve better results. To assess the quality of the initialization, add --evaluation flag.

3.2 Training

Use train.py to train Gaussians. Make sure that the initialization file *.npy has been generated.

# Training
python train.py -s <path to data>

# Example
python train.py -s XXX/0_chest_cone  # NeRF format
python train.py -s XXX/*.pickle  # NAF format

Command line arguments for train.py

Dataset and Model

--source_path / -s

Path to the source directory containing meta_data.json or *.pickle.

--model_path / -m

Path where the trained model should be stored (output/<random> by default).

--ply_path

Path to initialization point cloud *.npy. <path to data>/init_<data name>.npy by default.

--scale_min

Minimum scale of a Gaussian (expressed as a percentage of the volume size). 0.0005 by default.

--scale_max

Maximum scale of a Gaussian (expressed as a percentage of the volume size). 0.5 by default.

--eval

Add this flag to evaluate 2D rendering during training.

Optimizer

--iterations

Number of total iterations to train for, 30_000 by default.

--position_lr_init

Initial position learning rate, 0.0002 by default.

-position_lr_final

Initial position learning rate, 0.00002 by default.

--position_lr_max_steps

Number of steps (from 0) where position learning rate goes from initial to final. 30_000 by default.

--density_lr_init

Initial density learning rate, 0.01 by default.

--density_lr_final

Initial density learning rate, 0.001 by default.

--density_lr_max_steps

Number of steps (from 0) where density learning rate goes from initial to final. 30_000 by default.

--scaling_lr_init

Initial scaling learning rate, 0.005 by default.

--scaling_lr_final

Initial scaling learning rate, 0.0005 by default.

--scaling_lr_max_steps

Number of steps (from 0) where scaling learning rate goes from initial to final. 30_000 by default.

--rotation_lr_init

Initial rotation learning rate, 0.001 by default.

--rotation_lr_final

Initial rotation learning rate, 0.0001 by default.

--rotation_lr_max_steps

Number of steps (from 0) where rotation learning rate goes from initial to final. 30_000 by default.

--lambda_dssim

Weight of SSIM loss. 0.25 by default.

--lambda_tv

Weight of total variation loss. 0.05 by default.

--tv_vol_size

Size of tiny volume used for computing total variation. 32 by default.

--density_min_threshold

For adaptive control. Prune Gaussians with density less than this threshold. 0.00001 by default.

--densification_interval

How frequently to densify, 100 (every 100 iterations) by default.

--densify_from_iter

Iteration where densification starts, 500 by default.

--densify_until_iter

Iteration where densification stops, 15_000 by default.

--densify_grad_threshold

Limit that decides if points should be densified based on position gradient, 0.00005 by default.

--densify_scale_threshold

Densify Gaussians with 3D size larger than this threshold (expressed as a percentage of the volume size). 0.1 by default.

--max_screen_size

Prune Gaussians with 2D screen size larger than this threshold. None by default.

--max_scale

Prune Gaussians with 3D size larger than this threshold. None by default.

--max_num_gaussians

Stop denstification if Gaussians are more than this threshold. 500_000 by default.

Others

--test_iterations

Space-separated iterations at which the training script evaluate rendering and reconstruction performance over test set.

--save_iterations

Space-separated iterations at which the training script saves the Gaussian model.

--checkpoint_iterations

Space-separated iterations at which to store a checkpoint for continuing later, saved in the model directory.

--start_checkpoint

Path to a saved checkpoint to continue training from.

--quiet

Flag to omit any text written to standard out pipe.

--config

Path to *.yml file. If specified, overwrite other parameters.

You can also use scripts/train_all.py to train all cases in a folder.

# Example
python scripts/train_all.py \
  --source data/synthetic_dataset/cone_ntrain_50_angle_360 \
  --output output/synthetic_dataset/cone_ntrain_50_angle_360 \
  --device 0

❗ We scale the entire scene (scanner, projections, target volume) into a [-1,1]^3 space for numerical stability.

For our synthetic dataset (512x512 projections, 256x256x256 volume), the complete training process typically takes 5–15 minutes on an RTX 3090 GPU, with plausible results achievable in 3 minutes. The training time and model size depend on the object's structure. Sparser objects (e.g., a teapot) generally lead to faster training.

If training is too slow or there are too many Gaussians (>200k), consider adjusting the arguments, particularly those related to adaptive control.

3.3 Evaluation

We store evaluation results into the tensorboard events during training. You can also perform more detailed evaluation with test.py.

python test.py -m <path to trained model>

Command line arguments for test.py

--model_path / -m

Path where the trained model should be stored. output/<random> by default.

--source_path / -s

Path to the source directory containing meta_data.json or *.pickle. If not set, it will be automatically loaded from the model path.

--iterations

Iterations for evaluation. -1 (latest iteration) by default.

--skip_render_train

Flag to skip rendering the training set.

--skip_render_test

Flag to skip rendering the testing set.

--skip_recon

Flag to skip reconstructing the volume.

You can find all trained models here. We report quantitative results on all datasets (synthetic, real, and SAX-NeRF datasets) here.

4. Generate your own data

❗ Our code supports both cone beam and parallel beam configurations.

If you have ground truth volumes but do not have X-ray projections, follow this instruction to generate your own dataset.

If you have (more than 100) X-ray projections but do not have ground volumes, follow this instruction.

If you want to test your own data, please first convert it to our format (meta_data.json) or SAX-NeRF (*.pickle) and generate initialization point clouds with initialize_pcd.py.

5. Acknowledgement, license and citation

Our code is adapted from Gaussian Splatting, SAX-NeRF, NAF and TIGRE toolbox. We thank the authors for their excellent works.

This project is under the license of Gaussian Splatting.

If this repo helps you, please consider citing our work:

@inproceedings{r2_gaussian,
  title={R$^2$-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction},
  author={Ruyi Zha and Tao Jun Lin and Yuanhao Cai and Jiwen Cao and Yanhao Zhang and Hongdong Li},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year={2024}
}