Regularized Optimization Methods for Reconstruction and Modeling in Computer Graphics

The field of computer graphics deals with virtual representations of the real world. These can be obtained either through reconstruction of a model from measurements, or by directly modeling a virtual object, often on a real-world example. The former is often formalized as a regularized optimization problem, in which a data term ensures con-sistency between model and data and a regularization term promotes solutions that have high a priori probability. In this dissertation, different reconstruction problems in computer graphics are shown to be instances of a common class of optimization problems which can be solved using a uniform algorithmic framework. Moreover, it is shown that similar optimization methods can also be used to solve data-based modeling problems, where the amount of information that can be obtained from measurements is insufficient for accurate reconstruction