Auto-differentiable DRR rendering and optimization in PyTorch
DiffDRR
is a PyTorch-based digitally reconstructed radiograph (DRR) generator that provides
- Differentiable X-ray rendering
- GPU-accelerated synthesis and optimization
- 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:
- A fixed DRR from a set of ground truth parameters
- 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},
journal={arXiv preprint arXiv:2312.06358},
year={2023}
}