  Spectral methods are widely used in geometry processing of 3D models. They
rely on the projection of the mesh geometry on the basis defined by the
eigenvectors of the graph Laplacian operator, becoming computationally
prohibitive as the density of the models increases. In this paper, we propose a
novel approach for supporting fast and efficient spectral processing of dense
3D meshes, ideally suited for real-time compression and denoising scenarios. To
achieve that, we apply the problem of tracking graph Laplacian eigenspaces via
orthogonal iterations, exploiting potential spectral coherence between adjacent
parts. To avoid perceptual distortions when a fixed number of eigenvectors is
used for all the individual parts, we propose a flexible solution that
automatically identifies the optimal subspace size for satisfying a given
reconstruction quality constraint. Extensive simulations carried out with
different 3D meshes in compression and denoising setups, showed that the
proposed schemes are very fast alternatives of SVD based spectral processing
while achieving at the same time similar or even better reconstruction quality.
More importantly, the proposed approach can be employed by several other
state-of-the-art denoising methods as a preprocessing step, optimizing both
their reconstruction quality and their computational complexity.
