among all nd euclidean shapes carrying a degree of shade function, only those black and white ones, defined by a single polynomial inequality are determined by finitely many moments. in the single variable situation, a landmark moment transform discovered by a. markov untangles the above uniqueness feature. the 2d case is not less interesting, touching some spectral inverse problem for pairs of non-commuting self-adjoint transforms. a super-resolution phenomenon will be described in some detail with optimization and asymptotic expansion techniques.