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Topographical Tools for Filtering and Segmentation 2

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Mathematical morphology has developed a powerful methodology for segmenting images, based on connected filters and watersheds. We ... Weiterlesen
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Beschreibung

Mathematical morphology has developed a powerful methodology for segmenting images, based on connected filters and watersheds. We have chosen the abstract framework of node- or edge-weighted graphs for an extensive mathematical and algorithmic description of these tools.
Volume 2 proposes two physical models for describing valid flooding on a node- or edge-weighted graph, and establishes how to pass from one to another. Many new flooding algorithms are derived, allowing parallel and local flooding of graphs.
Watersheds and flooding are then combined for solving real problems. Their ability to model a real hydrographic basin represented by its digital elevation model constitutes a good validity check of the underlying physical models.
The last part of Volume 2 explains why so many different watershed partitions exist for the same graph. Marker-based segmentation is the method of choice for curbing this proliferation. This book proposes new algorithms combining the advantages of the previous methods which treated node- and edge-weighted graphs differently.



Fernand Meyer has been working at the Center for Mathematical Morphology of MINES ParisTech since 1975. He participated actively in the development of mathematical morphology, particularly in the field of segmentation and filtering.



Autorentext

Fernand Meyer has been working at the Center for Mathematical Morphology of MINES ParisTech since 1975. He participated actively in the development of mathematical morphology, particularly in the field of segmentation and filtering.



Inhalt

Notations xi

Introduction xxv

Part 1. Flooding 1

Chapter 1. Modelling Flooding in Edgeor Node-weighted Graphs 3

1.1. Summary of the chapter 3

1.2. The importance of flooding 4

1.2.1. Flooding creates lakes 4

1.2.2. Flooding for controlling watershed segmentation 4

1.2.3. Flooding, razing, leveling and flattening 5

1.3. Description of the flood covering a topographic surface 6

1.3.1. Observing the same flooding on two levels of abstraction 6

1.3.2. Modeling the two scales of flooding: at the pixel level or at the region level 7

1.3.3. Modeling a flooded topographic surface as a node-weighted graph 8

1.3.4. Modeling an edge-weighted graph as a tank network 15

1.4. The relations between n-floodings and e-floodings 19

1.4.1. Modeling flooding on two scales: the equivalence of both models 19

1.5. Flooding a flowing graph 21

1.5.1. Flowing graphs: reminder 21

1.5.2. Starting from an edge-weighted graph G[nil, ] 22

1.5.3. Starting from a node-weighted graph G[, nil] 24

1.5.4. Summarizing 24

Chapter 2. Lakes and Regional Minima 27

2.1. Summary of the chapter 27

2.2. Lakes from e-floodings and n-floodings 27

2.2.1. e-flooding of graphs G[nil, ] 27

2.2.2. n-flooding of graphs G[, nil] 28

2.3. Regional minimum lakes and full lakes 29

2.3.1. e-floodings of graphs G[nil, ] 29

2.3.2. n-floodings of graphs G[, nil] 30

2.4. Coherence between the definitions of lakes in G[, nil] and in G[nil, en] 31

Chapter 3. Among all Possible Floodings, Choosing One 33

3.1. Summary of the chapter 33

3.2. Various mechanisms for selecting a particular flooding 34

3.2.1. Dominated flooding in node- and edge-weighted graphs 34

3.2.2. Dominated flooding in node- and edge-weighted graphs 36

3.2.3. Dominated flooding as a function of the ceiling function 37

3.3. The topography of dominated flooding 37

3.3.1. The regional minima of dominated flooding in an edge-weighted graph G[nil, ] 38

3.3.2. The regional minima of dominated n-flooding in node-weighted graphs G[, nil] 39

3.3.3. Algorithmic consequences 41

3.4. Computing dominated flooding by local adjustments 43

3.4.1. The case of edge-weighted graphs G[nil, ] 43

3.4.2. The case of node-weighted graphs G[, nil] 44

3.4.3. Software or hardware implementation of Berge's algorithm 45

Chapter 4. Flooding and Flooding Distances 49

4.1. Summary of the chapter 49

4.2. Flooding distances 49

4.2.1. The flooding distance associated with the lakes of node- or edge-weighted graphs 49

4.2.2. Characterization of the flooding distance 50

4.2.3. Flooding distances on a graph or a tree 52

4.2.4. The shortest flooding distances 53

4.2.5. Dominated flooding and flooding distances 56

4.3. The shortest path algorithms for computing dominated flooding 66

4.3.1. Computing the shortest flooding distance with the MooreDijkstra algorithm 66

4.4. The flooding core-expanding algorithm 75

4.4.1. The first version of the core-expanding algorithm applied to the augmented graph GÂ 76

4.4.2. The second version of the core-expanding algorithm applied to the initial graph G 78

4.4.3. The third version of the core-expanding algorithm applied to the initial graph G 79

4.5. Marker-based segmentation 81

4.5.1. The case of a node-weighted graph G(, nil) 81

Chapter 5. Graph Flooding via Dendrograms 83

5.1. Summary of the chapter 83

5.2. Introduction 84

5.3. Den...

Produktinformationen

Titel: Topographical Tools for Filtering and Segmentation 2
Untertitel: Flooding and Marker-based Segmentation on Node- or Edge-weighted Graphs
Autor:
EAN: 9781119575153
Digitaler Kopierschutz: Adobe-DRM
Format: E-Book (pdf)
Hersteller: Wiley-ISTE
Genre: Elektronik, Elektrotechnik, Nachrichtentechnik
Anzahl Seiten: 284
Veröffentlichung: 23.01.2019
Dateigrösse: 15.0 MB