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We propose a spectral mean for closed curves described by sample points onits boundary subject to mis-alignment and noise. First, we ignore mis-alignmentand derive maximum likelihood estimators of the model and noise parameters inthe Fourier domain. We estimate the unknown curve by back-transformation andderive the distribution of the integrated squared error. Then, we modelmis-alignment by means of a shifted parametric diffeomorphism and minimise asuitable objective function simultaneously over the unknown curve and themis-alignment parameters. Finally, the method is illustrated on simulated dataas well as on photographs of Lake Tana taken by astronauts during a Shuttlemission.

A spectral mean for point sampled closed curves