Software


Papaya A 2D Minkowski Tensor Package	Karambola A 3D Minkowski Tensor Package	Pomelo A 3D Set Voronoi Diagrams Package
Papaya is a small program able to calculate the Minkowski Tensors of planar patterns. Papaya can use either polygon data as input or use the Marching Squares algorithm on image data. It can also perform a simple threshold segmentation. Minkowski Tensors can be calculated globally, or domain- and componentwise. A more detailed description of the program is given in the paper referenced below. Papaya is written in plain ISO C++ and a few (bundled) libraries. It is available as Free Software under the terms of the GNU General Public License, Version 3 or later.	Karambola is a program able to calculate the Minkowski Tensors of three-dimensional bodies and surfaces. Minkowski Tensors can be calculated globally, or for subsets (called “labels”). The program takes its input in the form of triangulated surfaces. A more detailed description of the program is given in the included documentation, and in the papers referenced below. Karambola is written in plain ISO C++ and only needs the GNU Scientific Library to compile. It is available as Free Software under the terms of the GNU General Public License, Version 3 or later.	Pomelo is a program to calculate 3D set voronoi diagrams for generic particles. Pomelo is designed to be as generic as possible. A detailed description can be found on github. Pomelo is written in modern C++11 and needs the Lua 5.2+ with respective devel packages. g++ 4.9.2 or clang++ 3.5.0-10 or higher is required. It is available as Free Software under the terms of the GNU General Public License, Version 3 or later.
Download Source code repository on GithubCurrent Release: Source code, version 1.8 Matlab Version: Jenny Wagner has developed a Matlab interface for Papaya. Older Releases: Source code, version 1.6 Source code, version 1.5 Source code, version 1.4 Source code, version 1.3	Download Current version described in Minkowski Tensors of Anisotropic Spatial Structure (see reference above): Source code (4.1 MB), New Journal of Phyics version	Download The current version can be found at github source code and various test cases (1.3 MB).
Contact sebastian.kapfer@fau.de	Contact karambola@physik.uni-erlangen.de	Contact simon.weis@fau.de philipp.schoenhoefer@fau.de
References Article describing the program: Gerd E. Schröder-Turk, Sebastian Kapfer, Boris Breidenbach, Claus Beisbart and Klaus Mecke Tensorial Minkowski functionals and anisotropy measures for planar patterns Journal of Microscopy 238(1), 57–74 (2010)	References The following articles describe the Minkowski Tensor Algorithms implemented by karambola: Minkowski Tensors of Anisotropic Spatial Structure, New Journal of Physics 15 (8), 083028 (2013) Robust Pore Size Analysis of Filamentous Networks from 3D Confocal Microscopy, Biophysical Journal 95 (12), pp. 6072–6080 Tensorial Minkowski functionals and anisotropy measures for planar patterns, Journal of Microscopy 238 (1) pp. 57–74 The following articles describe analyses of physical systems based on these concepts. Local Anisotropy of Fluids using Minkowski Tensors, Journal of Statistical Mechanics, P11010:1–20 (2010) Disordered spherical bead packs are anisotropic, EPL 90, 34001	References The following articles describe the Set Voronoi algorithm implemented in Pomelo.Set Voronoi diagrams of 3D assemblies of aspherical particles, Philosophical Magazine, Volume 93, Issue 31-33 (2013)