Abstract
Analysis of microscope images is a tedious work which requires patience and time, usually done manually by the microscopist after data collection. The results obtained in such a way might be biased by the human who performed the analysis. 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). As a result, the microscopic image is analyzed and the features on the image are automatically discovered, based on the local changes in Fourier Transform, without human bias. 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.
Highlights
Nowadays, due to digital data acquisition and storage, a huge amount of data is collected during microscopic imaging in the form of digital images from a single sample
We present a method based on a local moving window Fourier Transform and Machine Learning blind decomposition of the data via Non-Negative Matrix Factorization (NMF) (Smaragdis et al, 2014), which results in the successful automatic analysis of the local structure of various microscopic images within a minute on a standard notebook or desktop computer, without any external input
Another example is Scanning Electron Microscopy image of Au-rich morphology resulted from the temperature induced self-assembly process of 2 ML of Au deposited on clean GaSb(001) surface
Summary
Due to digital data acquisition and storage, a huge amount of data is collected during microscopic imaging in the form of digital images from a single sample. For the atomically resolved images approaches based on local crystallography and Machine Learning were developed (Belianinov et al, 2015; Vasudevan et al, 2015) They extract local information on material structure based on statistical analysis of atomic neighborhoods based on Fourier Transform followed by clustering and multivariate algorithms like Principal Component Analysis (PCA), Independent Component Analysis (ICA). In SPED a sample is scanned by focused electron beam and for each spatial pixel a full 2D diffraction is recorded, forming 4D data set i.e. two spatial dimensions related to scanning area and two reciprocal related to the diffraction Later, for this 4D data set the Machine Learning matrix decomposition methods are applied like NMF which can successfully extract local structure features, unmix and reduce dimensionality of complicated data. It is worth to notice that our approach in contrast to Neutral Network based approaches (e.g. Deep Learning) does not require any training datasets
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