  We present a simple and efficient method for refining maps or correspondences
by iterative upsampling in the spectral domain that can be implemented in a few
lines of code. Our main observation is that high quality maps can be obtained
even if the input correspondences are noisy or are encoded by a small number of
coefficients in a spectral basis. We show how this approach can be used in
conjunction with existing initialization techniques across a range of
application scenarios, including symmetry detection, map refinement across
complete shapes, non-rigid partial shape matching and function transfer. In
each application we demonstrate an improvement with respect to both the quality
of the results and the computational speed compared to the best competing
methods, with up to two orders of magnitude speed-up in some applications. We
also demonstrate that our method is both robust to noisy input and is scalable
with respect to shape complexity. Finally, we present a theoretical
justification for our approach, shedding light on structural properties of
functional maps.
