(284e) Quantimpy: Minkowski Functionals and Functions with Python

In nature, many examples can be found where geometry affects thermodynamics or the other way around. Examples include spinodal decomposition, Turing patterns, colloids, and porous media [7]. Recently, there has been a renewed interests to study these problems using Minkowski functionals and functions [1, 6, 9]. However, there is an apparent lack of well documented and easy to install libraries to compute the Minkowski functionals and functions in both 2D and 3D. In this talk we present the QuantImPy Python package. This package is inspired by and partly based on the QuantIm C/C++ library for scientific image processing [10]. This package can compute the Minkowski functionals of 2D or 3D binary images [8]. In addition, a variety of morphological distance maps based on the Euclidean distance transform [4] can be computed. These maps, in turn, can then be used to compute the Minkowski functions. Using Cython this package is fast and integrates natively with Numpy, the fundamental package for array computing with Python [5]. The code and documentation are available on Github [3], and the package has been published on PyPi for easy installation [2].

References
[1] R. T. Armstrong, J. E. McClure, V. Robins, Z. Liu, C. H. Arns, S. Schlüter, and S. Berg. Porous media characterization using minkowski functionals: Theories, applications and future directions. Transport in Porous Media, pages 1–31, 2018.
[2] A. M. P. Boelens. quantimpy pypi. https://pypi.org/project/quantimpy/, 2021.
[3] A. M. P. Boelens. Welcome to quantimpy’s documentation! https://boeleman.github.io/quantimpy, 2021.
[4] P. F. Felzenszwalb and D. P. Huttenlocher. Distance transforms of sampled functions. Theory of computing, 8(1):415–428, 2012.
[5] C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, et al. Array programming with numpy. Nature, 585(7825):357–362, 2020.
[6] A. G. Korpi, Ş. Ţălu, M. Bramowicz, A. Arman, S. Kulesza, B. Pszczolkowski, S. Jurečka, M. Mardani, C. Luna, P. Balashabadi, et al. Minkowski functional characterization and fractal analysis of surfaces of titanium nitride films. Materials Research Express, 6(8):086463, 2019.
[7] K. R. Mecke. Additivity, convexity, and beyond: applications of minkowski functionals in statistical physics. In Statistical Physics and Spatial Statistics, pages 111–184. Springer, 2000.
[8] J. Ohser and F. Mücklich. Statistical analysis of microstructures in materials science. Wiley and Sons, 2000.
[9] P. A. Slotte, C. F. Berg, and H. H. Khanamiri. Predicting resistivity and permeability of porous media using minkowski functionals. Transport in Porous Media, 131(2):705–722, 2020.
[10] H.-J. Vogel, U. Weller, and S. Schlüter. Quantification of soil structure based on minkowski functions. Computers & Geosciences, 36(10):1236–1245, 2010.