Measurement and analysis of point patterns in materials science: methods, applications, and prospects

Abstract The spatial distribution of material structures, defects, and microstructural features plays a crucial role in determining material properties such as mechanical strength, electrical conductivity, and thermal transport. Advances in high-resolution characterization techniques, such as atom probe tomography, now generate microscopy datasets with unprecedented precision and volume. These developments have created a growing need for robust statistical and metrological tools to quantify spatial organization in complex materials. Point Pattern Analysis (PPA) offers a powerful metrological framework to quantify these spatial arrangements, providing insights into clustering, ordering, and spatial correlations across multiple length scales. This review explores key PPA methodologies relevant to materials science, including distance, intensity and geometry -based approaches, while also exploring recent machine learning applications. The integration of modern computational approaches has further enhanced PPA’s ability to automate feature detection and predict microstructural transformations with greater precision. While challenges remain in handling large-scale datasets, experimental noise, and complex anisotropic structures, ongoing advancements in high-performance computing, artificial intelligence, and in-situ analysis continue to expand the applicability of PPA in materials science.