FastGeodis: Fast Generalised Geodesic Distance Transform

This repository provides CPU (OpenMP) and GPU (CUDA) implementations of Generalised Geodesic Distance Transform in PyTorch for 2D and 3D input data based on parallelisable raster scan ideas from [1]. It includes methods for computing Geodesic, Euclidean distance transform and mixture of both.

2D images, 1 of 4 passes	3D volumes, 1 of 6 passes

The above raster scan method can be parallelised for each row/plane on an available device (CPU or GPU). This leads to significant speed up as compared to existing non-parallelised raster scan implementations (e.g. https://github.com/taigw/GeodisTK). Python interface is provided (using PyTorch) for enabling its use in deep learning and image processing pipelines.

In addition, implementation of generalised version of Geodesic distance transforms along with Geodesic Symmetric Filtering (GSF) is provided for use in interactive segmentation methods, that were originally proposed in [1, 2, 5].

The raster scan based implementation provides a balance towards speed rather than accuracy of Geodesic distance transform and hence results in efficient hardware utilisation. On the other hand, in case of Euclidean distance transform, exact results can be achieved with other packages (albeit not on necessarilly on GPU) [6, 7, 8]

Citation

If you use this code in your research, then please consider citing:

Asad, Muhammad, Reuben Dorent, and Tom Vercauteren. "FastGeodis: Fast Generalised Geodesic Distance Transform." Journal of Open Source Software (JOSS), 2022. (paper link)

Bibtex:

@article{asad2022fastgeodis, 
  doi = {10.21105/joss.04532}, 
  url = {https://doi.org/10.21105/joss.04532}, 
  year = {2022}, 
  publisher = {The Open Journal}, 
  volume = {7}, 
  number = {79}, 
  pages = {4532}, 
  author = {Muhammad Asad and Reuben Dorent and Tom Vercauteren}, 
  title = {FastGeodis: Fast Generalised Geodesic Distance Transform}, 
  journal = {Journal of Open Source Software} 
}

Installation instructions

The provided package can be installed using:

pip install FastGeodis

pip install git+https://github.com/masadcv/FastGeodis

or (on conda environments with existing installation of PyTorch with CUDA)

pip install FastGeodis --no-build-isolation

Included methods

Optimised Fast Implementations for GPU/CPU based on [1]

Method	Description	Documentation
Fast Generalised Geodesic Distance 2D	Paralellised generalised geodesic distance transform for CPU/GPU [1]	FastGeodis.generalised_geodesic2d
Fast Generalised Geodesic Distance 3D	Paralellised generalised geodesic distance transform for CPU/GPU [1]	FastGeodis.generalised_geodesic3d
Fast Signed Generalised Geodesic Distance 2D	Paralellised signed generalised geodesic distance transform for CPU/GPU [1]	FastGeodis.signed_generalised_geodesic2d
Fast Signed Generalised Geodesic Distance 3D	Paralellised signed generalised geodesic distance transform for CPU/GPU [1]	FastGeodis.signed_generalised_geodesic3d
Fast Geodesic Symmetric Filtering 2D	Paralellised geodesic symmetric filtering for CPU/GPU [2]	FastGeodis.GSF2d
Fast Geodesic Symmetric Filtering 3D	Paralellised geodesic symmetric filtering for CPU/GPU [2]	FastGeodis.GSF3d

Toivanen's Implementations for CPU based on [9]

Method	Description	Documentation
Toivanen's Generalised Geodesic Distance 2D	Toivanen's generalised geodesic distance transform for CPU [9]	FastGeodis.generalised_geodesic2d_toivanen
Toivanen's Generalised Geodesic Distance 3D	Toivanen's generalised geodesic distance transform for CPU [9]	FastGeodis.generalised_geodesic3d_toivanen
Toivanen's Signed Generalised Geodesic Distance 2D	Toivanen's signed generalised geodesic distance transform for CPU [9]	FastGeodis.signed_generalised_geodesic2d_toivanen
Toivanen's Signed Generalised Geodesic Distance 3D	Toivanen's signed generalised geodesic distance transform for CPU [9]	FastGeodis.signed_generalised_geodesic3d_toivanen
Toivanen's Geodesic Symmetric Filtering 2D	Toivanen's geodesic symmetric filtering for CPU [2, 9]	FastGeodis.GSF2d_toivanen
Toivanen's Geodesic Symmetric Filtering 3D	Toivanen's geodesic symmetric filtering for CPU [2, 9]	FastGeodis.GSF3d_toivanen

Fast Marching Implementations for CPU based on [4, 10]

Method	Description	Documentation
Fast Marching Generalised Geodesic Distance 2D	Fast Marching generalised geodesic distance transform for CPU [9]	FastGeodis.generalised_geodesic2d_fastmarch
Fast Marching Generalised Geodesic Distance 3D	Fast Marching generalised geodesic distance transform for CPU [9]	FastGeodis.generalised_geodesic3d_fastmarch
Fast Marching Signed Generalised Geodesic Distance 2D	Fast Marching signed generalised geodesic distance transform for CPU [9]	FastGeodis.signed_generalised_geodesic2d_fastmarch
Fast Marching Signed Generalised Geodesic Distance 3D	Fast Marching signed generalised geodesic distance transform for CPU [9]	FastGeodis.signed_generalised_geodesic3d_fastmarch
Fast Marching Geodesic Symmetric Filtering 2D	Fast Marching geodesic symmetric filtering for CPU [2, 9]	FastGeodis.GSF2d_fastmarch
Fast Marching Geodesic Symmetric Filtering 3D	Fast Marching geodesic symmetric filtering for CPU [2, 9]	FastGeodis.GSF3d_fastmarch

Example usage

Fast Geodesic Distance Transform

The following demonstrates a simple example showing FastGeodis usage:

To compute Geodesic Distance Transform:

device = "cuda" if torch.cuda.is_available() else "cpu"
image = np.asarray(Image.open("data/img2d.png"), np.float32)

image_pt = torch.from_numpy(image).unsqueeze_(0).unsqueeze_(0)
image_pt = image_pt.to(device)
mask_pt = torch.ones_like(image_pt)
mask_pt[..., 100, 100] = 0

v = 1e10
# lamb = 0.0 (Euclidean) or 1.0 (Geodesic) or (0.0, 1.0) (mixture)
lamb = 1.0
iterations = 2
geodesic_dist = FastGeodis.generalised_geodesic2d(
    image_pt, mask_pt, v, lamb, iterations
)
geodesic_dist = np.squeeze(geodesic_dist.cpu().numpy())

To compute Euclidean Distance Transform:

device = "cuda" if torch.cuda.is_available() else "cpu"
image = np.asarray(Image.open("data/img2d.png"), np.float32)

image_pt = torch.from_numpy(image).unsqueeze_(0).unsqueeze_(0)
image_pt = image_pt.to(device)
mask_pt = torch.ones_like(image_pt)
mask_pt[..., 100, 100] = 0

v = 1e10
# lamb = 0.0 (Euclidean) or 1.0 (Geodesic) or (0.0, 1.0) (mixture)
lamb = 0.0
iterations = 2
euclidean_dist = FastGeodis.generalised_geodesic2d(
    image_pt, mask_pt, v, lamb, iterations
)
euclidean_dist = np.squeeze(euclidean_dist.cpu().numpy())

For more usage examples see:

Description	Python	Colab link
Simple 2D Geodesic and Euclidean Distance	`samples/simpledemo2d.py`
Simple Signed 2D Geodesic and Euclidean Distance	`samples/simpledemo2d_signed.py`
Simple 3D Geodesic and Euclidean Distance	`samples/simpledemo3d.py`
Simple Signed 3D Geodesic and Euclidean Distance	`samples/simpledemo3d_signed.py`
2D Geodesic Distance	`samples/demo2d.py`
2D Signed Geodesic Distance	`samples/demo2d_signed.py`
3D Geodesic Distance	`samples/demo3d.py`
3D Signed Geodesic Distance	`samples/demo3d_signed.py`
2D GSF Segmentation Smoothing	`samples/demoGSF2d_SmoothingSegExample.ipynb`

Unit Tests

A number of unittests are provided, which can be run as:

pip install -r requirements-dev.txt
python -m unittest

Documentation

Further details of each function implemented in FastGeodis can be accessed at the documentation hosted at: https://fastgeodis.readthedocs.io.

Contributing to FastGeodis

Spotted a bug or have a feature request to improve the package? We would love to have your input! See our guidelines for contributing.

Comparison of Execution Time and Accuracy

FastGeodis (CPU/GPU) is compared with existing GeodisTK (https://github.com/taigw/GeodisTK) in terms of execution speed as well as accuracy.

Execution Time

2D images	3D volumes

Accuracy

2D case

Qualitative Comparison	Quantitative (joint histogram)

3D case

Qualitative Comparison	Quantitative (joint histogram)

References

[1] Criminisi, Antonio, Toby Sharp, and Khan Siddiqui. "Interactive Geodesic Segmentation of n-Dimensional Medical Images on the Graphics Processor." Radiological Society of North America (RSNA), 2009. [pdf, ppt, url]
[2] Criminisi, Antonio, Toby Sharp, and Andrew Blake. "Geos: Geodesic image segmentation." European Conference on Computer Vision. Springer, Berlin, Heidelberg, 2008. [doi]
[3] Weber, Ofir, et al. "Parallel algorithms for approximation of distance maps on parametric surfaces." ACM Transactions on Graphics (TOG), (2008). [doi]
[4] GeodisTK: https://github.com/taigw/GeodisTK
[5] Criminisi, Antonio, Toby Sharp, Carsten Rother, and Patrick Pérez. "Geodesic image and video editing." ACM Trans. Graph. 29, no. 5 (2010): 134-1. [doi]
[6] https://github.com/seung-lab/euclidean-distance-transform-3d
[7] https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.distance_transform_edt.html
[8] https://www.tensorflow.org/addons/api_docs/python/tfa/image/euclidean_dist_transform
[9] Toivanen, Pekka J. "New geodosic distance transforms for gray-scale images." Pattern Recognition Letters 17.5 (1996): 437-450.
[10] Sethian, James A. "Fast marching methods." SIAM review 41.2 (1999): 199-235.

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