Estimating the size of an object captured with error

Abstract

In many applications we are faced with the problem of estimating object dimensions from a noisy image. Some devices like a fluorescent microscope, X-ray or ultrasound machines, etc., produce imperfect images. Image noise comes from a variety of sources. It can be produced by the physical processes of imaging, or may be caused by the presence of some unwanted structures (e.g. soft tissue captured in images of bones). In the proposed models we suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error. Here we use two one-dimensional parametric models to construct confidence intervals and statistical tests pertaining to the object size and suggest the possibility of application in two-dimensional problems. Normal and Laplace distributions are used as error distributions. Finally, we illustrate ability of the R-programs we created for these problems on a real-world example.

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Notes

  1. 1.

    As usual, \(z_{\alpha }\) is the \(1-\alpha \) quantile of standard normal distribution.

  2. 2.

    \(\chi ^{2}_{k,p}\) is the non-central \(\chi ^{2}\) distribution with k degree of freedom and non-centrality parameter p.

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Acknowledgements

We are very grateful to the anonymous referees for the valuable comments which have improved considerably the first version of the manuscript. This work is supported by the Croatian Science Foundation through research Grants IP-2016-06-6545.

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Correspondence to Kristian Sabo.

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This work is supported by the Croatian Science Foundation through research Grants IP-2016-06-6545.

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Hamedović, S., Benšić, M., Sabo, K. et al. Estimating the size of an object captured with error. Cent Eur J Oper Res 26, 771–781 (2018). https://doi.org/10.1007/s10100-017-0504-9

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Keywords

  • Noisy image
  • Additive error
  • Maximum likelihood estimator
  • Uniform distribution
  • Normal distribution
  • Laplace distribution