Euclidean Distance to Convex Polyhedra and Application to Class Representation in Spectral Images

With the aim of estimating the abundance map from observations only, linear unmixing approaches are not always suitable to spectral images, especially when the number of bands is too small or when the spectra of the observed data are too correlated. To address this issue in the general case, we present a novel approach which provides an adapted spatial density function based on any arbitrary linear classifier. A robust mathematical formulation for computing the Euclidean distance to polyhedral sets is presented, along with an efficient algorithm that provides the exact minimum-norm point in a polyhedron. An empirical evaluation on the widely-used Samson hyperspectral dataset demonstrates that the proposed method surpasses state-of-the-art approaches in reconstructing abundance maps. Furthermore, its application to spectral images of a Lithium-ion battery, incompatible with linear unmixing models, validates the method's generality and effectiveness.

Unsupervised Multi-Clustering and Decision-Making Strategies for 4D-STEM Orientation Mapping

This study presents a novel integration of unsupervised learning and decision-making strategies for the advanced analysis of 4D-STEM datasets, with a focus on non-negative matrix factorization (NMF) as the primary clustering method. Our approach introduces a systematic framework to determine the optimal number of components (k) required for robust and interpretable orientation mapping. By leveraging the K-Component Loss method and Image Quality Assessment (IQA) metrics, we effectively balance reconstruction fidelity and model complexity. Additionally, we highlight the critical role of dataset preprocessing in improving clustering stability and accuracy. Furthermore, our spatial weight matrix analysis provides insights into overlapping regions within the dataset by employing threshold-based visualization, facilitating a detailed understanding of cluster interactions. The results demonstrate the potential of combining NMF with advanced IQA metrics and preprocessing techniques for reliable orientation mapping and structural analysis in 4D-STEM datasets, paving the way for future applications in multi-dimensional material characterization.

Adaptative Diffraction Image Registration for 4D-STEM to optimize ACOM Pattern Matching

The technique known as 4D-STEM has recently emerged as a powerful tool for the local characterization of crystalline structures in materials, such as cathode materials for Li-ion batteries or perovskite materials for photovoltaics. However, the use of new detectors optimized for electron diffraction patterns and other advanced techniques requires constant adaptation of methodologies to address the challenges associated with crystalline materials. In this study, we present a novel image processing method to improve pattern matching in the determination of crystalline orientations and phases. Our approach uses sub-pixelar adaptative image processing to register and reconstruct electron diffraction signals in large 4D-STEM datasets. By using adaptive prominence and linear filters such as mean and gaussian blur, we are able to improve the quality of the diffraction pattern registration. The resulting data compression rate of 103 is well-suited for the era of big data and provides a significant enhancement in the performance of the entire ACOM data processing method. Our approach is evaluated using dedicated metrics, which demonstrate a high improvement in phase recognition. Our results demonstrate that this data preparation method not only enhances the quality of the resulting image but also boosts the confidence level in the analysis of the outcomes related to determining crystal orientation and phase. Additionally, it mitigates the impact of user bias that may occur during the application of the method through the manipulation of parameters.