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.

中文翻译：

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papaya2：二维不可约 Minkowski 张量计算

科学和技术领域的一个共同挑战是几何和形状的定量描述，例如在显微镜图像或天文观测数据的分析中。通常，希望超越标量形状指标，例如孔隙率和表面体积比，因为样品是各向异性的，或者因为感兴趣的方向相关量（例如电导或弹性）。闵可夫斯基张量是一个系统的通用和强大的高阶形状描述符系列，它允许任意阶的形状表征，并承诺为方向相关属性提供系统结构 - 函数关系的路径。Papaya2 是一种计算二维高阶形状度量的软件，具有库接口，支持不可约 Minkowski 张量和插值行进正方形。还提供了对 Matlab、JavaScript 和 Python 的扩展。虽然惯性张量是由许多工具计算的，但我们不知道其他开源软件在 2D 中提供更高阶的形状表征。