Automatic Microscopic Image Analysis by Moving Window Local Fourier Transform and Machine Learning

The microscopic image analysis is a tedious work which requires patience and time, usually done manually by microscopist after collecting the data. Here we introduce an approach of automatic image analysis, which is based on the locally applied Fourier Transform and Machine Learning methods. In this approach, the whole image is scanned by local moving window with defined size and the 2D Fourier Transform is calculated for each window. All the Local Fourier Transforms are fed into Machine Learning processing. Firstly, the number of components in the data is estimated from Principal Component Analysis (PCA) Scree Plot performed on the data. Secondly, the data are decomposed blindly by Non-Negative Matrix Factorization (NMF) into interpretable spatial maps (loadings) and corresponding Fourier Transforms (factors). Finally, the microscopic image is analyzed, the features on the image are automatically discovered, based on the local changes in Fourier Transform, without the human bias. The user selects only the size and movement of the scanning local window which defines the final analysis resolution. This automatic approach was successfully applied to analysis of various microscopic images with and without a local periodicity i.e. atomically resolved High Angle Annular Dark Field (HAADF) Scanning Transmission Electron Microscopy (STEM) image of Au nanoisland of fcc and Au hcp phases, Scanning Tunneling Microscopy (STM) image of Au-induced reconstruction on Ge(001) surface, Scanning Electron Microscopy (SEM) image of metallic nanoclusters grown on GaSb surface, and Fluorescence microscopy image of HeLa cell line of cervical cancer. The proposed approach could be used to automatically analyze the local structure of microscopic images within a time of ~minute for a single image on an average nowadays desktop/notebook computer and it is freely available as a Python analysis notebook.