Block-Based Spectral Processing of Static and Dynamic 3D Meshes using Orthogonal Iterations

Abstract: 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.