  Analysis of microscope images is a tedious work which requires patience and
time, usually done manually by the microscopist after data collection. Here we
introduce an approach of automatic image analysis, which is based on locally
applied Fourier Transform and Machine Learning methods. In this approach, a
whole image is scanned by a local moving window with defined size and the 2D
Fourier Transform is calculated for each window. Then, all the Local Fourier
Transforms are fed into Machine Learning processing. Firstly, a 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). The microscopic
image is analyzed and the features on the image are automatically discovered,
based on the local changes in Fourier Transform. The user selects only a 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 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 about a minute for a
single image on a modern desktop/notebook computer and it is freely available
as a Python analysis notebook and Python program for batch processing.
