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This repository provides the official code for the paper Shape from Projections via Differentiable Forward Projector for Computed Tomography published in Ultramicroscopy. The method estimates 3D shapes represented by a triangular mesh, directly from tomographic projection data. The basic idea of the method is to view tomographic reconstruction as a rendering process and extend a differentiable rasterizer [2] to optimize 3D shapes. Some parts of codes are ported from [2] with the comments of copyright form.

Simple examples through Colab notebook

  • ctdr_toy_example.ipynb Colab link : Simple mesh deformation example
  • ctdr_simulation.ipynb Colab link : Simulation of generating projections file from an obj file and a given projection geometry


Install requirements

The code requires python3 and Pytorch using CUDA on Linux. Install other requirements:

pip install trimesh
pip install h5py
pip install toml

If you have a problem on pymeshfix, try to install a recent version of numpy (e.g., pip install numpy==1.16.1).

(Optional) To refine the mesh, ctdr requires another package for obtaining watertight. Compile the watertight manifold code and copy the running file manifold into run folder. Lastly, you need to install

pip install pymeshfix

Install ctdr package

cd $ROOT # go to the root folder of the repository
pip install -e .

# compile cuda files
cd ctdr/cuda
python build_ext --inplace


To run the code, go to run folder and type:

python -data 2starA

where we run 2starA data. You can see available data files in data folder. You just need to input the directory name after -data. You can see all the parameters by typing python --help. For example, if you want to impose Gaussian noise with relative level 0.3, then run python -data 2spotA -eta 0.3.

If you want to refine the mesh (you should first install the required packages), as explained in the paper except for 2starA data, you can run:

python -data 2bob02A -niter0 -60

then, the method will refine the mesh at iteration 60, 120, 180. After finished, the results will be saved on result folder, including estimated projections, residuals and mesh files.

To run your own data, make a new folder in data and upload geometry information as proj_geom.toml and projection data file as sinogram.npy with the size of [angles x height x width]. You can refer to examples.

Demo for 2spotA data

Example of estimated projection images at iteration 0, 60, 120, 180

and the final estimated mesh from noisy input:


  • [1] Huang, Jingwei, Hao Su, and Leonidas Guibas. Robust Watertight Manifold Surface Generation Method for ShapeNet Models., arXiv preprint arXiv:1802.01698 (2018).
  • [2] Chen et al. Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer. NeurIPS, 2019.


This was funded by EU Horizon 2020 MSCA Innovative Training Network MUMMERING Grant Number 765604.


Direct 3D mesh reconstruction from tomographic projection data




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