Accounting for Location Measurement Error in Imaging Data With Application to Atomic Resolution Images of Crystalline Materials. Miller, M. J, Cabral, M. J, Dickey, E. C, LeBeau, J. M, & Reich, B. J Technometrics, 64(1):103–113, Taylor & Francis, January, 2022.
doi  abstract   bibtex   
AbstractScientists 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.
@ARTICLE{Miller2022-qm,
  title     = "Accounting for Location Measurement Error in Imaging Data With
               Application to Atomic Resolution Images of Crystalline Materials",
  author    = "Miller, Matthew J and Cabral, Matthew J and Dickey, Elizabeth C
               and LeBeau, James M and Reich, Brian J",
  abstract  = "AbstractScientists 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.",
  journal   = "Technometrics",
  publisher = "Taylor \& Francis",
  volume    =  64,
  number    =  1,
  pages     = "103--113",
  month     =  jan,
  year      =  2022,
  keywords  = "LeBeau",
  issn      = "0040-1706",
  doi       = "10.1080/00401706.2021.1905070"
}

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