Of Assembling Small Sculptures and Disassembling Large Geometry

Abstract

This thesis describes the research results and contributions that have been achieved during the author's doctoral work. It is divided into two independent parts, each of which is devoted to a particular research aspect.The first part covers the true-to-detail creation of digital pieces of art, so-called relief sculptures, from given 3D models. The main goal is to limit the depth of the contained objects with respect to a certain perspective without compromising the initial three-dimensional impression. Here, the preservation of significant features and especially their sharpness is crucial. Therefore, it is necessary to overemphasize fine surface details to ensure their perceptibility in the more complanate relief. Our developments are aimed at amending the flexibility and user-friendliness during the generation process. The main focus is on providing real-time solutions with intuitive usability that make it possible to create precise, lifelike and aesthetic results. These goals are reached by a GPU implementation, the use of efficient filtering techniques, and the replacement of user defined parameters by adaptive values. Our methods are capable of processing dynamic scenes and allow the generation of seamless artistic reliefs which can be composed of multiple elements.The second part addresses the analysis of repetitive structures, so-called symmetries, within very large data sets. The automatic recognition of components and their patterns is a complex correspondence problem which has numerous applications ranging from information visualization over compression to automatic scene understanding. Recent algorithms reach their limits with a growing amount of data, since their runtimes rise quadratically. Our aim is to make even massive data sets manageable. Therefore, it is necessary to abstract features and to develop a suitable, low-dimensional descriptor which ensures an efficient, robust, and purposive search. A simple inspection of the proximity within the descriptor space helps to significantly reduce the number of necessary pairwise comparisons. Our method scales quasi-linearly and allows a rapid analysis of data sets which could not be handled by prior approaches because of their size.