Generating high quality geometric representations from real-world objects is a fundamental problem in computer graphics which is motivated by manifold applications. They comprise image synthesis for movie production or computer games but also industrial applications such as quality assurance in mechanical engineering, the preservation of cultural heritage and the medical adaptation of prostheses or orthoses. Common demands of these applications on their underlying algorithms are robustness and efficiency. In addition, technological improvements of scanning devices and cameras which allow for the acquisition of new data types such as dynamic geometric data, create novel requirements which rise new challenges for processing algorithms.
This dissertation focuses on these aspects and presents different contributions for flexible, efficient and robust processing of static and time-varying geometric data. Two techniques focus on the problem of denoising. A statistical filtering algorithm for point cloud data building on non-parametric density estimation is introduced as well as a neighborhood filter for static and time-varying range data which is based on a novel non-local similarity measure. The third contribution unifies partition of unity decomposition and a global surface reconstruction algorithm based on the Fast Fourier Transform which results in a novel, robust and efficient reconstruction technique. Concluding, two flexible and versatile tools for designing scalar fields on meshes are presented which are useful to facilitate a controllable quadrangular remeshing.