Author Description

This dissertation, "Medial Axis Simplification Based on Global Geodesic Slope and Accumulated Hyperbolic Distance" by Rui, Wang,, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: The medial axis is an important shape representation and the computation of the medial axis is a fundamental research problem in computer graphics. Practically, the medial axis is widely used in various aspects of computer graphics, such as shape analysis, image segmentation, skeleton extraction and mesh generation and so forth. However, the applications of the medial axis have been limited by its sensitivity to boundary perturbations. This characteristic may lead to a number of noise branches and increase the complexity of the medial axis. To solve the sensitivity problem, it is critical to simplify the medial axis. This thesis first investigates the algorithms for computing medial axes of different input shapes. Several algorithms for the filtration of medial axes are then reviewed, such as the local importance measurement algorithms, boundary smoothness algorithms, and the global algorithms. Two novel algorithms for the simplification of the medial axis are proposed to generate a stable and simplified medial axis as well as its reconstructed boundary. The developed Global Geodesic Slope(GGS) algorithm for the medial axis simplification is based on the global geodesic slope defined in this thesis, which combines the advantages of the global and the local algorithms. The GGS algorithm prunes the medial axis according to local features as well as the relative size of the shape. It is less sensitive to boundary