Abstract
A common challenge in scientific and technical domains is the quantitative description of geometries and shapes, e.g. in the analysis of microscope imagery or astronomical observation data. Frequently, it is desirable to go beyond scalar shape metrics such as porosity and surface to volume ratios because the samples are anisotropic or because direction-dependent quantities such as conductances or elasticity are of interest. Minkowski Tensors are a systematic family of versatile and robust higher-order shape descriptors that allow for shape characterization of arbitrary order and promise a path to systematic structure-function relationships for direction-dependent properties. Papaya2 is a software to calculate 2D higher-order shape metrics with a library interface, support for Irreducible Minkowski Tensors and interpolated marching squares. Extensions to Matlab, JavaScript and Python are provided as well. While the tensor of inertia is computed by many tools, we are not aware of other open-source software which provides higher-rank shape characterization in 2D.
Highlights
Minkowski Tensors are a systematic family of versatile and robust higher-order shape descriptors, originating in integral geometry, see Schröder-Turk et al (2011) for an introduction and detailed references
A common challenge in scientific and technical domains is the quantitative description of geometries and shapes, e.g. in the analysis of microscope imagery or astronomical observation data
An accessible introduction to Minkowski Tensors can be found on www.morphometry.org
Summary
A common challenge in scientific and technical domains is the quantitative description of geometries and shapes, e.g. in the analysis of microscope imagery or astronomical observation data. We present papaya, a C++ library which facilitates computation of Irreducible Minkowski Tensors for two-dimensional geometries and shapes, including planar objects bounded by polygonal contours, collections of points (point patterns) and greyscale pixel data. This library is accompanied by example programs and bindings for Python, Matlab, and the JavaScript language. The C++ 11 library papaya contains the core algorithms to compute Irreducible Minkowski Tensors of two-dimensional geometries It processes both polygonal and 2D image input data. The demo ppanalysis exemplifies how to use this header file
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