The definition of microstructural features from an image is a challenge, given the uncertainty of the feature edges and the inherent user bias required in defining what is a feature. This challenge is particularly evident in atom probe tomography (APT), which captures tens of millions of atoms with their three-dimensional (3D) atomic position. Given the data uncertainty, issues with missing data, and dependency of the result on user-defined reconstruction, defining a relationship between the thermodynamic conditions and the resulting microstructure is difficult. Although numerous methods are capable of performing approximate clustering of precipitates, an accurate and fully automatic framework is still unavailable. In this paper, the authors present an advanced unsupervised machine learning framework that uses a graph-theoretic representation of the reconstructed 3D APT data and performs a modularity optimization to estimate an accurate cluster structure. The identified cluster structure can be used to estimate other geometrical properties and also the uncertainty in the precipitates. The authors demonstrate the approach to define and characterize the precipitates of an aluminum-magnesium-scandium sample, free of any user bias. The proposed unsupervised framework has been demonstrated to perform better than two well-known clustering methods. The approach described here was developed for APT data, but is developed in a generalized manner so as to be applicable to any point cloud data.

中文翻译：

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模块化优化，可使用3D原子化学规模成像来增强微结构特征中的边缘检测

考虑到特征边缘的不确定性以及定义什么是特征时需要的固有用户偏见，从图像定义微观结构特征是一个挑战。这一挑战在原子探针层析成像（APT）中尤为明显，该技术可捕获具有其三维（3D）原子位置的数千万个原子。给定数据的不确定性，数据丢失的问题以及结果对用户定义的重建的依赖性，很难定义热力学条件与所得微结构之间的关系。尽管许多方法都能够对沉淀物进行近似聚类，但仍然无法获得准确，全自动的框架。在本文中，作者提出了一种先进的无监督机器学习框架，该框架使用重建的3D APT数据的图形理论表示并执行模块化优化来估计准确的集群结构。所识别的团簇结构可用于估计其他几何性质以及沉淀物中的不确定性。作者演示了定义和表征铝-镁-dium样品沉淀物的方法，没有任何用户偏见。所提出的无监督框架已被证明比两种众所周知的聚类方法具有更好的性能。这里描述的方法是为APT数据开发的，但是是以通用的方式开发的，以便适用于任何点云数据。