Auto-differentiable DRR rendering and optimization in PyTorch

DiffDRR is a PyTorch-based digitally reconstructed radiograph (DRR) generator that provides

1. Differentiable X-ray rendering
2. GPU-accelerated synthesis and optimization
3. A pure Python implementation

Most importantly, DiffDRR implements DRR rendering as a PyTorch module, making it interoperable in deep learning pipelines.

To install the latest stable release (recommended):

pip install diffdrr

To install the development version:

git clone https://github.com/eigenvivek/DiffDRR.git --depth 1
pip install -e 'DiffDRR/[dev]'

The following minimal example specifies the geometry of the projectional radiograph imaging system and traces rays through a CT volume:

import matplotlib.pyplot as plt
import torch

from diffdrr.drr import DRR
from diffdrr.data import load_example_ct
from diffdrr.visualization import plot_drr

# Read in the volume and get its origin and spacing in world coordinates
subject = load_example_ct()

# Initialize the DRR module for generating synthetic X-rays
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
drr = DRR(
    subject,     # An object storing the CT volume, origin, and voxel spacing
    sdd=1020.0,  # Source-to-detector distance (i.e., focal length)
    height=200,  # Image height (if width is not provided, the generated DRR is square)
    delx=2.0,    # Pixel spacing (in mm)
).to(device)

# Set the camera pose with rotations (yaw, pitch, roll) and translations (x, y, z)
rotations = torch.tensor([[0.0, 0.0, 0.0]], device=device)
translations = torch.tensor([[0.0, 850.0, 0.0]], device=device)

# 📸 Also note that DiffDRR can take many representations of SO(3) 📸
# For example, quaternions, rotation matrix, axis-angle, etc...
img = drr(rotations, translations, parameterization="euler_angles", convention="ZXY")
plot_drr(img, ticks=False)
plt.show()

On a single NVIDIA RTX 2080 Ti GPU, producing such an image takes

25.2 ms ± 10.5 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

The full example is available at introduction.ipynb.

The physics-based pipeline in DiffDRR renders photorealistic X-rays. For example, compare a real X-ray to a synthetic X-ray rendered from a CT of the same patient using DiffDRR (X-rays and CTs from the DeepFluoro dataset):

The impotus for developing DiffDRR was to solve 2D/3D registration problems with gradient-based optimization. Here, we demonstrate DiffDRR's capabilities by generating two DRRs:

1. A fixed DRR from a set of ground truth parameters
2. A moving DRR from randomly initialized parameters

To align the two images, we use gradient descent to maximize an image similarity metric between the two DRRs. This produces optimization runs like this:

The full example is available at optimizers.ipynb.

For examples running DiffDRR on real surgical datasets, check out our latest work, DiffPose:

This work includes a lot of real-world usecases of DiffDRR including

• Using DiffDRR as a layer in a deep learning architecture
• Alignment of real X-rays and rendered DRRs
• Achieving sub-millimeter registration accuracy very quickly

DiffDRR can project 3D labelmaps into 2D simply using perspective geometry, helping identify particular structures in simulated X-rays (these labels come from the TotalSegmentator v2 dataset):

DiffDRR is differentiable with respect to the 3D volume as well as camera poses. Therefore, it could (in theory) be used for volume reconstruction via differentiable rendering. However, this feature has not been robustly tested and is currently under active development (see reconstruction.ipynb)!

DiffDRR source code, docs, and CI are all built using nbdev. To get set up with nbdev, install the following

mamba install jupyterlab nbdev -c fastai -c conda-forge 
nbdev_install_quarto  # To build docs
nbdev_install_hooks  # Make notebooks git-friendly

Running nbdev_help will give you the full list of options. The most important ones are

nbdev_preview  # Render docs locally and inspect in browser
nbdev_clean    # NECESSARY BEFORE PUSHING
nbdev_test     # tests notebooks
nbdev_export   # builds package and builds docs

For more details, follow this in-depth tutorial.

DiffDRR reformulates Siddon’s method,¹ an exact algorithm for calculating the radiologic path of an X-ray through a volume, as a series of vectorized tensor operations. This version of the algorithm is easily implemented in tensor algebra libraries like PyTorch to achieve a fast auto-differentiable DRR generator.

If you find DiffDRR useful in your work, please cite our paper:

@inproceedings{gopalakrishnan2022fast,
  title={Fast auto-differentiable digitally reconstructed radiographs for solving inverse problems in intraoperative imaging},
  author={Gopalakrishnan, Vivek and Golland, Polina},
  booktitle={Workshop on Clinical Image-Based Procedures},
  pages={1--11},
  year={2022},
  organization={Springer}
}

If the 2D/3D registration capabilities are helpful, please cite our followup, DiffPose:

@article{gopalakrishnan2023intraoperative,
  title={Intraoperative {2D/3D} image registration via differentiable {X}-ray rendering},
  author={Gopalakrishnan, Vivek and Dey, Neel and Golland, Polina},
  booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  pages={11662--11672},
  year={2024}
}