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