Simplifying The Non-Manifold Topology Of Multi-Partitioning Surface Networks

Abstract

In bio-medical imaging, multi-partitioning surface networks (MPSNs) are very useful to model complex organs with multiple anatomical regions, such as a mouse brain. However, MPSNs are usually constructed from image data and might contain complex geometric and topological features. There has been much research on reducing the geometric complexity of a general surface (non-manifold or not) and the topological complexity of a closed, manifold surface. But there has been no attempt so far to reduce redundant topological features which are unique to non-manifold surfaces, such as curves and points where multiple sheets of surfaces join. In this thesis, we design interactive and automated means for removing redundant non-manifold topological features in MPSNs, which is a special class of non-manifold surfaces. The core of our approach is a mesh surgery operator that can effectively simplify the non-manifold topology while preserving the validity of the MPSN. The operator is implemented in an interactive user interface, allowing user-guided simplification of the input. We further develop an automatic algorithm that invokes the operator following a greedy heuristic. The algorithm is based on a novel, abstract representation of a non-manifold surface as a graph, which allows efficient discovery and scoring of possible surgery operations without the need for explicitly performing the Type of Report: MS Thesis Department of Computer Science & Engineering Washington University in St. Louis Campus Box 1045 St. Louis, MO 63130 ph: (314) 935-6160 WASHINGTON UNIVERSITY IN ST. LOUIS School of Engineering and Applied Science Department of Computer Science and Engineering Thesis Examination Committee: Tao Ju, Chair Robert Pless Jeremy Buhler SIMPLIFYING THE NON-MANIFOLD TOPOLOGY OF MULTI-PARTITIONING SURFACE NETWORKS by Trung Duc Nguyen A thesis presented to the School of Engineering of Washington University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE May 2011 Saint Louis, Missouri ABSTRACT OF THE THESISOF THE THESIS Simplifying the Non-Manifold Topology of Multi-Partitioning Surface Networks by Trung Duc Nguyen Master of Science in Computer Science Washington University in St. Louis, 2011 Research Advisor: Professor Tao Ju In bio-medical imaging, multi-partitioning surface networks (MPSNs) are very useful to model complex organs with multiple anatomical regions, such as a mouse brain. However, MPSNs are usually constructed from image data and might contain complex geometric and topological features. There has been much research on reducing the geometric complexity of a general surface (non-manifold or not) and the topological complexity of a closed, manifold surface. But there has been no attempt so far to reduce redundant topological features which are unique to non-manifold surfaces, such as curves and points where multiple sheets of surfaces join. In this thesis, we design interactive and automated means for removing redundant non-manifold topological features in MPSNs, which is a special class of non-manifold surfaces. The core of our approach is a mesh surgery operator that can effectively simplify the non-manifold topology while preserving the validity of the MPSN. The operator is implemented in an interactive user interface, allowing user-guided simplification of the input. We further develop an automatic algorithm that invokes the