Adaptive wavelets based multiresolution modeling of irregular meshes via harmonic maps

We propose an adaptive wavelets based multiresolution scheme by using harmonic maps for 3D irregular meshes. This approach extends the previous works by M. Eck et al. (see SIGGRAPH \´95, p.173-82, 1995) and M. Lounsbery (see "Multiresolution Analysis for Surfaces of Arbitrary Topological Type", PhD thesis, Department of Computer Science and Engineering, University of Washington, p.129, 1994) which have been developed for regular triangular mesh subdivision. First, we construct parameterizations of the original mesh that results in a remesh having a subdivision connectivity for the wavelets decomposition. Next, the local subdivision based multiresolution scheme is presented. Our algorithm represents effectively a region of interest or a region having complex and high curvature geometry by using bi-orthogonal wavelets. Through the computer simulation tested on some example meshes, we show that the proposed method is more effective than the previous regular subdivision methods