Variational methods for geometry processing

Abstract

Inspired by the success of variational techniques in various

applications such as image processing and recent advance in sparse norm minimization, this research explores a class of variational methods with sparse norm for digital geometry processing which has to deal with noisy data and non-smooth features. The variational model mainly contains two terms: one is to keep the intrinsic properties of the function and the other is to make the function satisfy some prior knowledge. Three types of geometry processing problems are studied under the similar variational framework. The research focuses on the specific formulation of the variational model and efficient numerical solvers. Its objective is to develop novel geometry processing algorithms that can effectively and robustly process geometric models characterized by the co-existence

of non-smooth features and noise/outliers, which is usually

difficult in prior art.