Return to search

Medial axis simplification based on global geodesic slope and accumulated hyperbolic distance

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 noises than the local algorithms, and can maintain the features of the shape in highly concave regions while the global algorithms may not.



The other simplification algorithm we propose is the Accumulated Hyperbolic Distance(AHD) algorithm. It directly uses the evaluation criterion of the error, accumulated hyperbolic distance defined in this thesis, as the pruning measurement in the filtration process. It guarantees the upper bound of the error between the reconstructed shape and the original one within the defined threshold. The AHD algorithm avoids sudden changes of the reconstructed shape as the defined threshold changes. / published_or_final_version / Computer Science / Master / Master of Philosophy

  1. 10.5353/th_b4833013
  2. b4833013
Identiferoai:union.ndltd.org:HKU/oai:hub.hku.hk:10722/173883
Date January 2012
CreatorsWang, Rui, 王睿
ContributorsChan, KP, Wang, WP
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Source SetsHong Kong University Theses
LanguageEnglish
Detected LanguageEnglish
TypePG_Thesis
Sourcehttp://hub.hku.hk/bib/B48330139
RightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works., Creative Commons: Attribution 3.0 Hong Kong License
RelationHKU Theses Online (HKUTO)

Page generated in 0.0018 seconds