The medial axis, or topological skeleton, of an object Ω is the set of all points in Ω having more than one closest point on the object boundary, ∂Ω. This repository contains matlab code for computing the medial axis of binary images.
A binary image is one with only two pixel values or colors. This code (and all examples) use the convention that the two image colors are black and white, with pixel values 0 and 1 respectively.
The algorithm works on solid, filled in shapes (like the black horse above), as well as thin contours (see Examples section below).
In both cases, the medial axis is only computed in white regions; i.e. Ω is considered to be all white pixels in the image, and all black pixels are merely treated as object boundaries, or part of ∂Ω. See Usage below for more details.
To download the code, open a terminal and type:
git clone https://github.com/mrezanejad/AOFSkeletons.git
This will create a directory AOFSkeletons/ containing all of the code seen here.
To compute the Skeleton of a single image, one can use our matlab function generate_skeletons. Navigate to the downloaded AOFSkeletons/ folder and from the matlab console run:
>> generate_skeletons('path/to/your/image.png')
The skeleton for image.png will be computed and saved to skeleton.png. Any standard image format can be used.
NOTE: The algorithm only computes the skeleton for white regions in the image. One can compute the skeleton in black regions by setting the optional invert argument to true,
>> generate_skeletons('path/to/your/image.png`, 'invert', true)
This is particulary useful if the input image is of a solid black object on a white background (like the horse above).
To save the generated skeleton to an image file, use the optional argument skeleton_path, followed by an output image path:
>> generate_skeletons('path/to/your/image.png', 'skeleton_path', 'path/to/save/skeleton.png')
You can generate the horse example shown above using the included image images/horse_1.png. Note the horse is solid black on a white bacground, so to generate the interior skeleton of the black region we will have to use the optional invert argument:
>> generate_skeletons('images/horse_1.png', 'images/horse_1_skeleton_int.png', 'invert', true)
By leaving out the invert option, we could also generate the skeleton of the background (white region):
>> generate_skeletons('images/horse_1.png', 'images/horse_1_skeleton_ext.png')
Skeletons of Line Drawings
As mentioned above,the algorithm also works for line drawings, or contour drawings. These are drawings of scenes with thin black lines outlining objects, such as the city scene below. The objects are not filled in, unlike in the horse example; we can then compute the medial axis for all white pixels in the image, with the black contours as the object boundary:
>> generate_skeletons('images/city_1.png', 'images/city_1_skeleton')
No inversion is necessary since the contours are black already.
For faster performance, one can compile the .m matlab scripts included here to MEX binaries.
Open matlab and navigate to AOFSkeletons/. In the console, run:
>> compile_mex
This will create a folder codegen/, which contains auto-generate C code for the relevant .m files, which is then compiled to MEX.
Assuming you have not made any local changes to these files, you can update your local code to the newest version with git pull.
Open a terminal, navigate to your AOFSkeletons/ folder, and run
git pull
If you have edited any files, git pull may throw errors. You can update while keeping your local changes by running:
git stash
git pull
git stash pop
If you are new to git, you can learn more about it here
If you use the AOF Skeleton package, we appreciate it if you cite the following papers:
@incollection{rezanejad2013flux,
title={Flux graphs for 2D shape analysis},
author={Rezanejad, Morteza and Siddiqi, Kaleem},
booktitle={Shape Perception in Human and Computer Vision},
pages={41--54},
year={2013},
publisher={Springer}
}
@inproceedings{dimitrov2003flux,
title={Flux invariants for shape},
author={Dimitrov, Pavel and Damon, James N and Siddiqi, Kaleem},
booktitle={Computer Vision and Pattern Recognition, 2003. Proceedings. 2003 IEEE Computer Society Conference on},
volume={1},
pages={I--I},
year={2003},
organization={IEEE}
}
@article{Siddiqi:2002:HS:598432.598510,
author = {Siddiqi, Kaleem and Bouix, Sylvain and Tannenbaum, Allen and Zucker, Steven W.},
title = {Hamilton-Jacobi Skeletons},
journal = {Int. J. Comput. Vision},
issue_date = {July-August 2002},
volume = {48},
number = {3},
month = jul,
year = {2002},
issn = {0920-5691},
pages = {215--231},
numpages = {17},
url = {https://doi.org/10.1023/A:1016376116653},
doi = {10.1023/A:1016376116653},
acmid = {598510},
publisher = {Kluwer Academic Publishers},
address = {Norwell, MA, USA},
keywords = {2D and 3D skeletons, Hamiltonian systems, eikonal equation, flux and divergence, shape analysis},
}
For any question regarding this package, please contact morteza@cim.mcgill.ca
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.