A spectral mean for random closed curves

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Abstract

We propose a spectral mean for closed sets described by sample points on their boundaries subject to mis-alignment and noise. We derive maximum likelihood estimators for the model and noise parameters in the Fourier domain. We estimate the unknown mean boundary curve by back-transformation and derive the distribution of the integrated squared error. Mis-alignment is dealt with by means of a shifted parametric diffeomorphism. The method is illustrated on simulated data and applied to photographs of Lake Tana taken by astronauts during a Shuttle mission. We propose a spectral mean for closed sets described by sample points on their boundaries subject to mis-alignment and noise. We derive maximum likelihood estimators for the model and noise parameters in the Fourier domain. We estimate the unknown mean boundary curve by back-transformation and derive the distribution of the integrated squared error. Mis-alignment is dealt with by means of a shifted parametric diffeomorphism. The method is illustrated on simulated data and applied to photographs of Lake Tana taken by astronauts during a Shuttle mission.
Original languageUndefined
Pages (from-to)72-85
Number of pages14
JournalSpatial statistics
Volume18
Issue numberPart A
DOIs
Publication statusPublished - Nov 2016

Keywords

  • EWI-27110
  • Spectral analysis
  • Missing data
  • IR-102382
  • Random closed set
  • METIS-319436
  • Image analysis

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