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.

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Persistent URL dx.doi.org/10.1016/j.spasta.2016.02.002
Journal Spatial Statistics
van Lieshout, M.N.M. (2016). A spectral mean for random closed curves. Spatial Statistics, 18 Part A, 72–85. doi:10.1016/j.spasta.2016.02.002