Spectral estimation of Gaussian random circles and spheres

A maximum a posteriori estimator is presented for estimating the parameters of a lognormal random field defined on the unit circle S1. The measurement data are star-like curves, sample functions that are insufficiently known as equivalent classes of plane curves, where a curve is determined except translations and rotations in R2. The estimation problem is also considered in the case of a lognormal random field defined on the unit sphere S2, where the measurements are sample function surfaces, determined except translations and rotations in R3.