The Gradient Product Transform (GPT) is an algorithm that assigns a symmetry score to each pixel in a grayscale image. This score values can be used for detecting symmetric objects or for extracting medial axes, e.g. from blood vessels.
This code implements the algorithm described in (cited as "IPOL paper" below):
C. Dalitz, J. Wilberg: "The Gradient Product Transform: An Image Filter for Symmetry Detection." Image Processing On Line, 9 (2019), pp. 413–431 https://doi.org/10.5201/ipol.2019.270
Please cite this article when using the code. The article was published on IPOL with version 1.1 of this code. For changes since then, see the file CHANGES.
Building the code requires cmake and a standard C++98 (or later) compiler. We have tested the code with gcc 5.4.0, LLVM 9.0.0, and MSVC 14.1.
The number of kernels used for parallel computation can be set by the variable NUM_THREADS in CMakeLists.txt. Parallelization requires OpenMP to be installed. While OpenMP is supported by default on Linux, it must must be installed manually on OSX with "brew install libomp". Moreover, at least cmake version 3.12 is required for OpenMP support on OSX and for MSVC, whilst on other platforms cmake 3.5 is sufficient.
Before running cmake, you should adjust the variable NUM_THREADS in CMakeLists.txt to the number of kernels on your system.
Starting from the root directory (i.e., the directory, in which this Readme file is located), the executable "gptsymmetry" is created with:
mkdir build
cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make
To test the program, you can apply it to the test image included in this source package as follows:
gptsymmetry -r 80 -o result.png ../testimage.png
This will mark the detected symmetries in the result image file "result.png".
The command line program gptsymmetry reads a PNG image, prints the detected symmetries to stdout and optionally writes images showing a skeleton of symmetry axes and of the detected symmetric objects.
Calling gptsymmetry without any or with an unknown option (e.g. "-?") will print a usage message. The meaning of the parameters controlling the algorithm is explained in the IPOL paper.
The input file must be in PNG format. With the option "-o ", the detected symmetry regions are darwn into the image and written to . Unless the option "-notrace" is given, three additional images are written:
trace-symmetry.png
the GPT symmetry score converted to grayscaletrace-ridges.png
skeletons of symmetry axestrace-localmaxpoints.pngthe symmetry regions classified into axial (red) an rotational (cyan)
The detected symmetry regions are printed to stdout in the following format:
rot;x;y;rx;ry;S;s_norm
0;142;317;5;23;5044167.206566;0.903770
0;141;325;5;14;4800286.097710;0.947354
1;295;198;32;33;4569864.069128;0.784917
0;106;298;38;42;3361987.012759;0.720138
where "rot" indicates rotational (1) or axial (0) symmetry, (x,y) is the center and (rx,ry) the size of the symmetry region, S is the GPT score, and s_norm is the normalized GPT score between zero and one. Thus, to report only rotational symmetries, you can pipe the output to grep as follows:
gptsymmetry -r 100 -notrace test.png | grep '^1'
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png++/this is a copy of libpng++ version 0.2.9 from https://www.nongnu.org/pngpp/ with two modifications to error.hpp:- fix for bug #46312 applied
- strerror_r redifened as strerror_s for MSVC compiler
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main.cppMain program that implmenting Algorithms 1-3 (sections 2 & 3 in the IPOL paper) -
point.hImplements types and function related to 2D points. -
image.[h|cpp]Implements three image types (Gray, RGB, Float) -
image_processing.[h|cpp] -
symmetry_transform.[h|cpp]Implementats functions for individual steps in Algorithms 1-3 of the IPOL paper.
Christoph Dalitz, Jens Wilberg, 2019 Institute for Pattern Recognition Niederrhein University of Applied Sciences Krefeld, Germany
The software includes the library png++ by Alexander Shulgin, available from https://www.nongnu.org/pngpp/. See the directory src/png++ for details.