Area-Preserving Parameterization with Tutte Regularization

Area-preserving parameterization is now widely applied, such as for remeshing and medical image processing. We propose an efficient and stable approach to compute area-preserving parameterization on simply connected open surfaces. From an initial parameterization, we construct an objective function of energy. This consists of an area distortion measure and a new regularization, termed as the Tutte regularization, combined into an optimization problem with sliding boundary constraints. The original area-preserving problem is decomposed into a series of subproblems to linearize the boundary constraints. We design an iteration framework based on the augmented Lagrange method to solve each linear constrained subproblem. Our method generates a high-quality parameterization with area-preserving on facets. The experimental results demonstrate the efficacy of the designed framework and the Tutte regularization for achieving a fine parameterization.