Smooth reverse subdivision

In this paper we present a new multiresolution framework that takes into consideration reducing the coarse points’ energy during decomposition. We start from initial biorthogonal filters to include energy minimization in multiresolution. Decomposition and reconstruction are main operations for any multiresolution representation. We formulate decomposition as smooth reverse subdivision, based on a least squares problem. Both approximation of overall shape and energy are taken into account in the least squares formulation through different weights.Using this method, significant smoothness in decomposition of curves and tensor product surfaces can be achieved; while their overall shape is preserved. Having smooth coarse points yields details with maximum characteristics. Our method works well with synthesizing applications in which re-using high-energy details is important. We use our method for finding the smooth reverse of three common subdivision schemes. We also provide examples of our method in curve synthesis and terrain synthesis applications.