Modularity optimization for enhancing edge detection in microstructural features using 3D atomic chemical scale imaging

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.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 es...