  We consider the problem of localizing relevant subsets of non-rigid geometric
shapes given only a partial 3D query as the input. Such problems arise in
several challenging tasks in 3D vision and graphics, including partial shape
similarity, retrieval, and non-rigid correspondence. We phrase the problem as
one of alignment between short sequences of eigenvalues of basic differential
operators, which are constructed upon a scalar function defined on the 3D
surfaces. Our method therefore seeks for a scalar function that entails this
alignment. Differently from existing approaches, we do not require solving for
a correspondence between the query and the target, therefore greatly
simplifying the optimization process; our core technique is also
descriptor-free, as it is driven by the geometry of the two objects as encoded
in their operator spectra. We further show that our spectral alignment
algorithm provides a remarkably simple alternative to the recent
shape-from-spectrum reconstruction approaches. For both applications, we
demonstrate improvement over the state-of-the-art either in terms of accuracy
or computational cost.
