```
import matplotlib.pyplot as plt
import torch
from diffdrr.data import load_example_ct
from diffdrr.drr import DRR
from diffdrr.visualization import plot_drr
# Read in the volume and get the isocenter
= load_example_ct()
volume, spacing = torch.tensor(volume.shape) * torch.tensor(spacing) / 2
bx, by, bz
# Initialize the DRR module for generating synthetic X-rays
= "cuda" if torch.cuda.is_available() else "cpu"
device = DRR(
drr # The CT volume as a numpy array
volume, # Voxel dimensions of the CT
spacing, =300.0, # Source-to-detector radius (half of the source-to-detector distance)
sdr=200, # Height of the DRR (if width is not seperately provided, the generated image is square)
height=4.0, # Pixel spacing (in mm)
delx
).to(device)
# Set the camera pose with rotation (yaw, pitch, roll) and translation (x, y, z)
= torch.tensor([[torch.pi, 0.0, torch.pi / 2]], device=device)
rotation = torch.tensor([[bx, by, bz]], device=device)
translation
# 📸 Also note that DiffDRR can take many representations of SO(3) 📸
# For example, quaternions, rotation matrix, axis-angle, etc...
= drr(rotation, translation, parameterization="euler_angles", convention="ZYX")
img =False)
plot_drr(img, ticks plt.show()
```

# DiffDRR

Auto-differentiable DRR synthesis and optimization in PyTorch

`DiffDRR`

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

- Auto-differentiable DRR syntheisis
- GPU-accelerated rendering
- A pure Python implementation

Most importantly, `DiffDRR`

implements DRR synthesis as a PyTorch module, making it interoperable in deep learning pipelines.

## Installation Guide

To install `DiffDRR`

from PyPI:

`pip install diffdrr`

`DiffDRR`

also requires `PyTorch3D`

, which gives us the ability to use multiple parameterizations of SO(3) when constructing camera poses! For most users,

`conda install pytorch3d -c pytorch3d`

should work perfectly well. Otherwise, see PyTorch3D’s installation guide.

### Development (optional)

`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_prepare # NECESSARY BEFORE PUSHING: builds package, tests notebooks, and builds docs in one step
```

For more details, follow this in-depth tutorial.

## Usage

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

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

`33.3 ms ± 6.78 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)`

The full example is available at `introduction.ipynb`

.

## Application: 6-DoF Slice-to-Volume Registration

We demonstrate the utility of our auto-differentiable DRR generator by solving a 6-DoF registration problem with gradient-based optimization. Here, we generate two DRRs:

- A fixed DRR from a set of ground truth parameters
- A moving DRR from randomly initialized parameters

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

The full example is available at `optimizers.ipynb`

.

## How does `DiffDRR`

work?

`DiffDRR`

reformulates Siddon’s method,^{1} the canonical 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.

## Citing `DiffDRR`

If you find `DiffDRR`

useful in your work, please cite our paper (or the freely accessible arXiv version):

```
@inproceedings{gopalakrishnanDiffDRR2022,
author = {Gopalakrishnan, Vivek and Golland, Polina},
title = {Fast Auto-Differentiable Digitally Reconstructed Radiographs for Solving Inverse Problems in Intraoperative Imaging},
year = {2022},
booktitle = {Clinical Image-based Procedures: 11th International Workshop, CLIP 2022, Held in Conjunction with MICCAI 2022, Singapore, Proceedings},
series = {Lecture Notes in Computer Science},
publisher = {Springer},
doi = {https://doi.org/10.1007/978-3-031-23179-7_1},
}
```