Smooth reverse Loop and Catmull–Clark subdivision

In this paper we present a new multiresolution technique for general topology surfaces based on reversing subdivision with energy minimization. We first introduce a general reverse subdivision approach that starts from a trial set of biorthogonal multiresolution filters and refines the resulting coarse points using local masks. The refinement step tries to find a good approximation of the fine points while minimizing the local energy of the coarse points in a least-squares sense. This approach is then used to find smooth reverse of the Loop and Catmull–Clark subdivisions. We discuss the advantages of using this technique in various surface editing and synthesis applications.