A PDE patch-based spectral method for progressive mesh compression and mesh denoising

The development of the patchwise partial differential equation (PDE) framework a few years ago has paved the way for the PDE method to be used in mesh signal processing. In this paper, we, for the first time, extend the use of the PDE method to progressive mesh compression and mesh denoising. We, meanwhile, upgrade the existing patchwise PDE method in patch merging, mesh partitioning, and boundary extraction to accommodate mesh signal processing. In our new method, an arbitrary mesh model is partitioned into patches, each of which can be represented by a small set of coefficients of its PDE spectral solution. Since low-frequency components contribute more to the reconstructed mesh than high-frequency ones, we can achieve progressive mesh compression and mesh denoising by manipulating the frequency terms of the PDE solution. Experimental results demonstrate the feasibility of our method in both progressive mesh compression and mesh denoising.