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Morphological Modeling of Terrains and Volume Data 2014 ed. [Mīkstie vāki]

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  • Formāts: Paperback / softback, 116 pages, height x width: 235x155 mm, weight: 2058 g, 58 Illustrations, black and white; XI, 116 p. 58 illus., 1 Paperback / softback
  • Sērija : SpringerBriefs in Computer Science
  • Izdošanas datums: 28-Oct-2014
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 1493921487
  • ISBN-13: 9781493921485
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  • Mīkstie vāki
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Morphological Modeling of Terrains and Volume Data 2014 ed.Palielināt
  • Formāts: Paperback / softback, 116 pages, height x width: 235x155 mm, weight: 2058 g, 58 Illustrations, black and white; XI, 116 p. 58 illus., 1 Paperback / softback
  • Sērija : SpringerBriefs in Computer Science
  • Izdošanas datums: 28-Oct-2014
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 1493921487
  • ISBN-13: 9781493921485
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781493921485.html
Keywords:
This book describes the mathematical background behind discrete approaches to morphological analysis of scalar fields, with a focus on Morse theory and on the discrete theories due to Banchoff and Forman. The algorithms and data structures presented are used for terrain modeling and analysis, molecular shape analysis, and for analysis or visualization of sensor and simulation 3D data sets. It covers a variety of application domains including geography, geology, environmental sciences, medicine and biology. The authors classify the different approaches to morphological analysis which are all based on the construction of Morse or Morse-Smale decompositions. They describe algorithms for computing such decompositions for both 2D and 3D scalar fields, including those based on the discrete watershed transform. Also addressed are recent developments in the research on morphological shape analysis, such as simplification operators for Morse and Morse-Smale complexes and their multi-resolution representation. Designed for professionals and researchers involved with modeling and algorithm analysis, Morphological Modeling of Terrains and Volume Data is a valuable resource. Advanced-level students of computer science, mathematics and geography will also find the content very helpful.
1 Background
1(24)
1.1 Some Preliminary Definitions
1(6)
1.1.1 Manifolds
2(1)
1.1.2 Cell Complexes
3(1)
1.1.3 Regular Grids and Simplicial Complexes
4(2)
1.1.4 Primal and Dual Complex
6(1)
1.2 Models for Scalar Fields
7(2)
1.3 Morse Theory and Morse Complexes
9(4)
1.4 Watershed Transform in the Smooth Case
13(1)
1.5 Piecewise-Linear Morse Theory
14(3)
1.5.1 Critical Points in a Piecewise-Linear Model
14(2)
1.5.2 Quasi-Morse-Smale Complexes
16(1)
1.6 Forman Theory
17(4)
1.7 Summary
21(4)
References
22(3)
2 Morphology Computation Algorithms: Generalities
25(12)
2.1 Classification of Morphology Computation Algorithms
26(3)
2.1.1 Input Dimension, Format and Properties
26(1)
2.1.2 Output Information and Its Format
26(1)
2.1.3 Algorithmic Approach
27(2)
2.2 Detection of Critical Points
29(4)
2.2.1 Detecting Critical Points in a Simplicial Model
29(3)
2.2.2 Detecting Critical Points in a Regular Grid
32(1)
2.3 Handling the Domain Boundary
33(1)
2.4 Presence of Plateaus
33(4)
References
35(2)
3 Boundary-Based and Region-Growing Algorithms
37(22)
3.1 Boundary-Based Algorithms
38(12)
3.1.1 Boundary-Based Methods on Simplicial Models
38(7)
3.1.2 Analysis and Comparisons
45(3)
3.1.3 Boundary-Based Methods on Regular Grids
48(2)
3.2 Region-Growing Algorithms
50(9)
3.2.1 The Two Algorithms by Danovaro et al
51(2)
3.2.2 The Algorithm by Magillo et al
53(2)
3.2.3 The Algorithm by Gyulassy et al
55(1)
3.2.4 Analysis and Comparisons
56(1)
References
57(2)
4 Watershed Algorithms
59(10)
4.1 Watershed by Simulated Immersion
60(2)
4.2 Watershed by Topographic Distance
62(2)
4.3 Watershed by Rain Falling Simulation
64(2)
4.4 Summary and Comparisons
66(3)
References
67(2)
5 A Combinatorial Approach Based on Forman Theory
69(20)
5.1 Representing Morse Complexes in the Discrete Case
70(3)
5.1.1 Representing Discrete Ascending and Descending Morse Complexes
70(2)
5.1.2 Representing the Discrete Morse-Smale Complex
72(1)
5.2 Encoding the Forman Gradient
73(2)
5.2.1 Encoding Triangle and Tetrahedral Meshes
73(1)
5.2.2 Compact Gradient Encoding
74(1)
5.3 Computing the Forman Gradient
75(6)
5.3.1 Forman Approach Based on Connolly's Function
76(1)
5.3.2 A Forman-Based Approach for Tetrahedral Meshes
77(1)
5.3.3 The Algorithm by Gyulassy et al
78(2)
5.3.4 The Algorithm by Robins et al
80(1)
5.4 Computing Discrete Morse and Morse-Smale Complexes
81(4)
5.4.1 Descending Morse Complex
82(1)
5.4.2 Ascending Morse Complex
82(2)
5.4.3 Morse-Smale Complex
84(1)
5.4.4 Morse Incidence Graph
84(1)
5.5 Summary and Comparisons
85(4)
References
87(2)
6 Simplification and Multi-Resolution Representations
89(16)
6.1 Simplification Operators
89(5)
6.1.1 cancellation Operator
90(2)
6.1.2 remove Operator
92(1)
6.1.3 Comparison of cancellation and remove Operators
93(1)
6.2 Multi-Resolution Models
94(8)
6.2.1 Models for 2D Scalar Fields
95(1)
6.2.2 A Multi-Resolution Morphological Model for Arbitrary Scalar Fields
96(3)
6.2.3 A Combined Morphological and Geometrical Multi-Resolution Model for Triangulated Terrains
99(3)
6.3 Summary
102(3)
References
103(2)
7 Experimental Analysis and Comparisons
105
7.1 Different Output Formats
105(2)
7.2 Metrics for Comparison
107(1)
7.3 Comparing Watershed and Forman-Based Approaches
108(2)
7.4 Comparing All Approaches in 2D
110(2)
7.4.1 Comparison on Models Without Flat Edges
110(1)
7.4.2 Handling Flat Edges
110(2)
7.5 Summary
112
References
115