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Digital Morse Theory With Suggested Applications
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Contents
1. ABSTRACT.
2. Table of Contents
Contents
3. List of Figures
List of Figures
4. List of Tables
List of Tables
5. Introduction
6. Toward a Digital Morse Theory: Preliminaries.
6.1 Traditional Morse Theory cannot be directly applied.
6.2 Relaxing Morse conditions with combinatorial insight.
6.3 Why edge-connectivity is insufficient.
6.4 Making the correct choice for diagonal adjacency.
7. Digital Morse Theory.
7.1 Axiomatic treatment of level set boundary interpolation problem.
7.2 Consequences of axioms: critical points, sets, and values.
8. A criticality graph: from peaks, pits, and passes to peers, parents, and progeny (ppp -> PPP)
8.1 Criticality graph and zone of influence definitions
8.2 Properties of the criticality graph and zones.
9. Algorithmic issues.
9.1 A hypersurface construction algorithm.
9.2 The criticality graph and zone of influence algorithm.
9.3 Correctness of criticality graph and zone of influence algorithm.
10. Applications of the theory and algorithms
10.1 Criticality graph and data simplification and organization.
10.2 Criticality graph, zones, and fast rendering.
10.3 Characterizing genus changes at criticalities.
10.4 Topology preserving simplification.
10.5 Managing Level of Detail.
10.6 Finding criticalities in high dimensional datasets.
10.7 Applications to X-ray crystallography.
10.8 Applications to multi-modal Image registration.
11. Conclusion and Future Work
Bibliography
12. Tables and Figures
12.1 Tables
12.2 Figures
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Digital Morse Theory With Suggested Applications
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Super-User
1999-02-01
