1-ring interpolatory wavelet using function vectors for mobile computing

As an effective tool for the multiresolution rendering and editing for the complex models and scenes, the wavelet transforms attract more and more attention in recent years. While, the usual wavelet transforms developed for the mesh simplification still have some problems in the efficiency or shape preservation. They either consume much time and memory in the wavelet analysis, or generate low-detailed versions of models with the unwilling sharp convex edges. In this paper, we propose a novel and efficient wavelet transform based on the matrix-valued 1-ring interpolatory subdivision. Our matrix-valued wavelet transform is constructed on the function vectors, which makes it suitable for processing the vector-valued signals. Different from the usual multivariate wavelets, each component of the vector-valued signals processed by the matrix-valued wavelet are correlated. The resulted meshes are influenced by each component of the vector, which provides a way to adjust the shape of meshes. To overcome the defect that 1-ring subdivision surfaces is too sensitive to the initial shape control parameters, we develop a general approach to determine the shape control parameters for the subdivision and the wavelet transform, so making the multiresolution surfaces stable and smooth. We adopt the local lifting scheme to make the wavelet transform more efficient and low memory cost. The experiments have shown that our wavelet transform is efficient and stable, with the good shape-preserving ability. These features make it especially suitable for the resource-limited mobile computing.