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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 photographsdoi:10.1016/j.spasta.2016.02.002 fatcat:tcaizrlvmzgt3kvxs2etcykute