STEMax_PF: accurate and fast peak-finding for atom quantitative analysis

Abstract

Aberration-Corrected Scanning Transmission Electron Microscopy (AC-STEM) offers sub-ångström resolution and has become the most microscopic and advanced tool in the field of materials science, yet its quantitative image analysis has been constrained by high computational demands, uneven background illumination, and challenges in resolving overlapping point spread functions. In this work, we introduce STEMax_PF, a novel software tool that integrates and improves multiple advanced techniques - including an adaptive threshold-enhanced centroid method, rapid normalized cross-correlation for detecting light atoms, and an improved weighted overdetermined regression algorithm - to effectively address these issues. In the two-dimensional Gaussian fitting process, STEMax_PF adopts a unique strategy by individually estimating the initial fitting parameters for each atomic column using several approaches, ensuring accurate fitting for materials comprising any elements. The integration of these methods dramatically reduces computational resource usage and enables extremely fast processing. Furthermore, STEMax_PF is universally applicable to any crystal structure and STEM image format, paving the way for reliable quantitative atomic analysis and its connection to phenomena such as ferroelectric polarization, piezoelectric/dielectric responses, and electron-phonon interactions.

Keywords

STEM / peak finding / quantitative atomic analysis

References

[1] Pennycook SJ.High-resolution incoherent imaging of crystals.Phys Rev Lett1990;64:938-41

[2] Pennycook S.Atomic resolution Z-contrast imaging of interfaces.Acta Metallurgica et Materialia1992;40:S149-59

[3] Qu W,Yang Y.Atomic-level quantitative analysis of electronic functional materials by aberration-corrected STEM.Chinese Phys B33:116802

[4] Wang Y,Sigle W,van Aken PA.Oxygen octahedra picker: a software tool to extract quantitative information from STEM images.Ultramicroscopy2016;168:46-52

[5] Nord M,MacLaren I,Holmestad R.Atomap: a new software tool for the automated analysis of atomic resolution images using two-dimensional Gaussian fitting.Adv Struct Chem Imag2017;3:9 PMCID:PMC5306439

[6] Rekik A,Benjelloun M.A k-Means clustering algorithm initialization for unsupervised statistical satellite image segmentation.2006 1ST IEEE International Conference on E-Learning in Industrial Electronics IEEE Publishers:Piscataway, New Jersey, USA, 2006; pp 11-6

[7] Boyat AK. A review paper: noise models in digital image processing. arXiv: arXiv:1505.03489v1 [Preprint]. 2015 [cited 2017 Feb 9]: [13 p.]. Available from: https://doi.org/10.48550/arXiv.1505.03489

[8] Cheezum MK,Guilford WH.Quantitative comparison of algorithms for tracking single fluorescent particles.Biophys J2001;81:2378-88 PMCID:PMC1301708

[9] Lin R,Wang C,Xin HL.TEMImageNet training library and AtomSegNet deep-learning models for high-precision atom segmentation, localization, denoising, and deblurring of atomic-resolution images.Sci Rep2021;11:5386

[10] Nan H,Ma X.Application of sliding window algorithm with convolutional neural network in high-resolution electron microscope image.J Chin Electr Microsc Soc2021;40:242-50. (in Chinese)

[11] Bradley D.Adaptive thresholding using the integral image.J Graphics Tools2007;12:13-21

[12] Okunishi E,Sawada H,Hori M.Visualization of light elements at ultrahigh resolution by STEM annular bright field microscopy.Microsc Microanal2009;15:164-5

[13] Born M. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed.; Cambridge University Press; 1999.

[14] Hu MK.Visual pattern recognition by moment invariants.IRE Trans Inf Theory1962;8:179-87

[15] Sneath PHA. Numerical Taxonomy (by) Peter H.A. Sneath (and) Robert R. Sokal: The Principles and Practice of Numerical Classification; W.H. Freeman and Company, 1973.

[16] Viola O.Robust real-time face detection.Int J Comput Vis2004;57:137-54

[17] Lewis JP. Fast Template Matching. In Vision Interface 95, Proceedings of the Canadian Image Processing and Pattern Recognition Society, Quebec City, Canada; May 15-19, 1995; Canadian Image Processing and Pattern Recognition Society: Québec, Canada, 1995; pp 15-9.http://scribblethink.org/Work/nvisionInterface/vi95_lewis.pdf (accessed 2025-11-26)

[18] Shafait F,Breuel TM.Efficient implementation of local adaptive thresholding techniques using integral images. In IS&T/SPIE International Symposium on Electronic Imaging, Proceedings of the 15th Conference on Document Recognition and Retrieval, San Jose, USA; January 26-31, 2008; SPIE: San Jose, USA, 2008; pp 681510.

[19] Frank J,Eisenberg D.Reconstruction of glutamine synthetase using computer averaging.Ultramicroscopy1978;3:283-90 PMCID:PMC4167717

[20] Lewis,JP. Fast normalized crosscorrelation. San Rafael, CA: Industrial Light & Magic; 1995. https://www.researchgate.net/publication/2378357_Fast_Normalized_Cross-Correlation (accessed 2025-6-4)

[21] Shapiro LG. Computer and Robot Vision; Vol 2 Reading, MA: AddisonWesley Publishing Company, 1992

[22] Teukolsky SA,Flannery BP. Numerical Recipes: The Art of Scientific Computing, 3rd ed.; Cambridge University Press; 2007

[23] Nobach H. Two-dimensional Gaussian regression for sub-pixel displacement estimation in particle image velocimetry or particle position estimation in particle tracking velocimetry.Exp Fluids2005;38:511-5

[24] Anthony SM.Image analysis with rapid and accurate two-dimensional gaussian fitting.Langmuir2009;25:8152-60

[25] Sigworth F. Read .dm3 and .dm4 image files. MATLAB Central File Exchange. Accessed December 23, 2024. https://www.mathworks.com/matlabcentral/fileexchange/43005-read-dm3-and-dm4-image-files (accessed 2025-6-4)

[26] Mitchell DRG. Create a Synthetic HAADF Image. Version 20211129, v1.2 [Source code] http://dmscripting.com/create_a_synthetic_haadf_image.html (accessed 2025-6-4)

[27] Bosman M,García-Muñoz JL,Findlay SD.Two-dimensional mapping of chemical information at atomic resolution.Phys Rev Lett2007;99:086102

[28] Mevenkamp N,Dahmen W,Yankovich AB.Poisson noise removal from high-resolution STEM images based on periodic block matching.Adv Struct Chem Imag2015;1:4

[29] Jones L.Identifying and correcting scan noise and drift in the scanning transmission electron microscope. Microsc Microanal 2013;19:1050-60.

[30] Bals S,Van Tendeloo G.Statistical estimation of atomic positions from exit wave reconstruction with a precision in the picometer range.Phys Rev Lett2006;96:096106

[31] Mitchell DRG. Atomic Displacement. Version 20230104, v2.1 [Source code] http://dmscripting.com/atomic_displacement.html (accessed 2025-6-4)

[32] Total Resolution. *Tempas* (Version 3.0.42) [Software]. 2023. https://www.totalresolution.com/Tempas.htm

[33] Zhang Y,Li S.Phase interface engineering enables state-of-the-art half-Heusler thermoelectrics.Nat Commun2024;15:5978 PMCID:PMC11252142