Accounting for Location Measurement Error in Imaging Data With Application to Atomic Resolution Images of Crystalline Materials

Abstract

Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance. Current measurement error methods require an estimate or knowledge of the measurement error variance to correct these estimates, which may not be available. Instead, we create a spatial Bayesian hierarchical model that treats the locations as parameters, using the image itself to incorporate positional uncertainty. We lower the computational burden by approximating the likelihood using a noncontiguous block design around the object locations. We use this model to quantify the relationship between the intensity and displacement of hundreds of atom columns in crystal structures directly imaged via scanning transmission electron microscopy (STEM). Atomic displacements are related to important phenomena such as piezoelectricity, a property useful for engineering applications like ultrasound. Quantifying the sign and magnitude of this relationship will help materials scientists more precisely design materials with improved piezoelectricity. A simulation study confirms our method corrects bias in the estimate of the parameter of interest and drastically improves coverage in high noise scenarios compared to non-measurement error models.

Keywords:

• Bayesian hierarchical modeling
• Materials science
• Scanning transmission electron microscopy
• Spatial statistics
• Image analysis

Acknowledgments

AIF is a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), a site in the National Nanotechnology Coordinated Infrastructure (NNCI).

Supplementary Materials

Supplementary file:

Supplement to “Accounting for Location Measurement Error in Imaging Data with Application to Atomic Resolution Images of Crystalline Materials”. This file includes additional details on finding initial atom column locations, justification for model choices, hypothesis testing using stochastic search variable selection, sensitivity analysis and MCMC derivations. (pdf)

Computer code:

Code for MCMC, simulation, and figures for spatial Bayesian hierarchical model accounting for measurement error in Scanning Transmission Electron Microscope (STEM) images. (zip file containing R scripts and RData file with imaging data)

Additional information

Funding

This material is based upon work supported by the National Science Foundation under Grant No. DGE-1633587. MJC, ECD, and JML gratefully acknowledge support for this work from the National Science Foundation, as part of the Center for Dielectrics and Piezoelectrics under Grant Nos. IIP-1361571 and IIP-1361503. This work was performed in part at the Analytical Instrumentation Facility (AIF) at North Carolina State University, which is supported by the State of North Carolina and the National Science Foundation (ECCS-1542015).