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Topographical tools for filtering and segmentation. . 2 Flooding and marker-based segmentation on node- or edge-weighted graphs / / Fernand Meyer
| Topographical tools for filtering and segmentation. . 2 Flooding and marker-based segmentation on node- or edge-weighted graphs / / Fernand Meyer |
| Autore | Meyer Fernand <1952-> |
| Pubbl/distr/stampa | London, United Kingdom : , : ISTE, Ltd. |
| Descrizione fisica | 1 online resource |
| Disciplina | 551.4 |
| Collana | Digital signal and image processing series |
| Soggetto topico |
Relief models
Topographical drawing |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-119-57515-X
1-119-57513-3 1-119-57512-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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, η] 22 -- 1.5.3. Starting from a node-weighted graph G[ν, 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, η] 27 -- 2.2.2. n-flooding of graphs G[ν, nil] 28 -- 2.3. Regional minimum lakes and full lakes 29 -- 2.3.1. e-floodings of graphs G[nil, η] 29 -- 2.3.2. n-floodings of graphs G[ν, nil] 30 -- 2.4. Coherence between the definitions of lakes in G[ν, nil] and in G[nil, δenν] 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, η] 38.
3.3.2. The regional minima of dominated n-flooding in node-weighted graphs G[ν, 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, η] 43 -- 3.4.2. The case of node-weighted graphs G[ν, 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 Moore-Dijkstra 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(ν, nil) 81 -- Chapter 5. Graph Flooding via Dendrograms 83 -- 5.1. Summary of the chapter 83 -- 5.2. Introduction 84 -- 5.3. Dendrograms: reminder 86 -- 5.3.1. The structure associated with an order relation 86 -- 5.3.2. Dendrograms 87 -- 5.3.3. Stratification index and partial ultrametric distances (PUD) 88 -- 5.4. The hierarchy of lake zones 89 -- 5.4.1. The lake zones of an edge-weighted graph G(nil, η) 89 -- 5.4.2. The hierarchy of lake zones, i.e. the closed balls of χ 92 -- 5.4.3. Representing of hierarchy of lake zones 94 -- 5.5. The law of communicating vessels 98 -- 5.5.1. The flooding levels in connected subgraphs and closed balls 99. 5.6. Dominated flooding on the dendrogram of lake zones 100 -- 5.6.1. Notations 100 -- 5.6.2. Incidence of the ceiling function on the dendrogram flooding levels 100 -- 5.6.3. Finding the flooding level of a leaf 102 -- 5.6.4. Parallel processing for flooding the dendrogram 105 -- 5.6.5. Strategies for flooding the dendrogram of lake zones 106 -- 5.7. Constructing and flooding a binary dendrogram 111 -- 5.7.1. Two dendrograms representing the same hierarchy 111 -- 5.7.2. Constructing a binary dendrogram representing a hierarchy 112 -- 5.7.3. Flooding a binary dendrogram 113 -- 5.8. A derived algorithm for dominated flooding 113 -- 5.8.1. Algorithm “ancestor-flood without constructing the dendrogram” 117 -- 5.8.2. Illustration 117 -- Part 2. Modeling a Real Hydrographic Basin 119 -- Chapter 6. The Hydrographic Basin of a Digital Elevation Model 121 -- 6.1. Summary of the chapter 121 -- 6.2. Preprocessing the digital elevation model 121 -- 6.2.1. Suppressing the spurious regional minima 121 -- 6.2.2. Creating an ∞ − steep digraph 123 -- 6.2.3. Local pruning for extracting marked rivers 126 -- 6.2.4. Extracting all rivers 128 -- 6.2.5. Labeling sources and rivers 129 -- 6.2.6. Detection of crest lines 131 -- 6.2.7. Detecting the upstream of sources 132 -- 6.2.8. Analyzing the tree structure of rivers 133 -- 6.2.9. Constructing the catchment zones of riverlets 137 -- Part 3. Watershed Partitions 139 -- Chapter 7. Minimum Spanning Forests and Watershed Partitions 141 -- 7.1. Summary of the chapter 141 -- 7.2. Flooding distance, minimum spanning trees and forests 142 -- 7.2.1. Flooding distances 142 -- 7.2.2. Flooding distance on the minimum spanning tree of the graph G(nil, η) 143 -- 7.2.3. Characterizing the MST 145 -- 7.3. Minimum spanning forests rooted in markers 146 -- 7.3.1. Constructing the minimum spanning forest 147 -- 7.3.2. Converting the minimum spanning forest into a minimum spanning tree 149 -- 7.4. Watershed partitions of weighted graphs 150. 7.4.1. Catchment basins and watershed partitions 150 -- 7.4.2. Flowing paths and catchment basins 151 -- 7.5. Minimum spanning forests rooted in the regional minima 151 -- 7.5.1. A minimum spanning forest corresponds to each watershed partition 151 -- 7.5.2. Inversely, each watershed partition spans a minimum spanning forest 154 -- 7.5.3. A rather unexpected watershed partition 156 -- 7.6. A manifold of different watershed partitions 159 -- 7.6.1. Catchment zones and catchment basins 159 -- 7.7. Reducing the number of watershed partitions 160 -- 7.7.1. Minimum spanning forests of k - steep or ∞ − steep graphs 163 -- 7.7.2. The waterfall hierarchy 168 -- 7.7.3. Usefulness of the waterfall hierarchy 171 -- Chapter 8. Marker-based Segmentation 175 -- 8.1. Dominated flooding and minimum spanning forests 177 -- 8.1.1. Dominated flooding 177 -- 8.1.2. Minimum spanning forests 177 -- 8.1.3. Illustration 178 -- 8.1.4. Minimum spanning forests and dominated flooding 179 -- 8.2. Constructing a minimum spanning forest rooted in the markers 183 -- 8.2.1. Algorithms for constructing a minimum spanning forest 183 -- 8.2.2. Increasing the selectiveness of Prim’s algorithm 186 -- 8.2.3. Marker-based segmentation of node-weighted graphs 187 -- 8.2.4. Derived algorithms 190 -- 8.3. Marker-based segmentation after flooding the graph 194 -- 8.3.1. Segmenting the dominated flooding of a graph 194 -- 8.3.2. The case of an edge-weighted graph 194 -- 8.3.3. Constructing a k - steep or ∞ − steep watershed partition for a node-weighted graph G(ν, nil) 200 -- 8.4. Directly constructing a marker-based ∞ − steep watershed partition with the core expanding algorithm 201 -- 8.5. The early days of marker-based segmentation 202 -- 8.5.1. The level-by-level construction of a watershed 203 -- 8.6. A two scale marker-based segmentation 205 -- 8.7. Instant marker-based segmentation 205 -- 8.7.1. Why and when we need instant marker-based segmentation 205 -- 8.7.2. The reef and cascade distance 206. 8.7.3. Computing the reef and cascade distance for all pairs of nodes in G(nil, η) 209 -- 8.7.4. Computing the smallest reef and cascade distances between all couples of nodes in a graph 212 -- Conclusion 217 -- Appendix 227 -- References 239 -- Index 241. |
| Altri titoli varianti | Flooding and marker-based segmentation on node- or edge-weighted graphs |
| Record Nr. | UNINA-9910467622703321 |
Meyer Fernand <1952->
|
||
| London, United Kingdom : , : ISTE, Ltd. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topographical tools for filtering and segmentation . 2 Flooding and marker-based segmentation on node- or edge-weighted graphs / / Fernand Meyer
| Topographical tools for filtering and segmentation . 2 Flooding and marker-based segmentation on node- or edge-weighted graphs / / Fernand Meyer |
| Autore | Meyer Fernand <1952-> |
| Pubbl/distr/stampa | London : , : ISTE, Ltd. |
| Descrizione fisica | 1 online resource (289 pages) |
| Disciplina | 551.4 |
| Collana |
Digital signal and image processing series
THEi Wiley ebooks. |
| Soggetto topico |
Relief models
Topographical drawing |
| ISBN |
1-119-57515-X
1-119-57513-3 1-119-57512-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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, η] 22 -- 1.5.3. Starting from a node-weighted graph G[ν, 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, η] 27 -- 2.2.2. n-flooding of graphs G[ν, nil] 28 -- 2.3. Regional minimum lakes and full lakes 29 -- 2.3.1. e-floodings of graphs G[nil, η] 29 -- 2.3.2. n-floodings of graphs G[ν, nil] 30 -- 2.4. Coherence between the definitions of lakes in G[ν, nil] and in G[nil, δenν] 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, η] 38.
3.3.2. The regional minima of dominated n-flooding in node-weighted graphs G[ν, 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, η] 43 -- 3.4.2. The case of node-weighted graphs G[ν, 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 Moore-Dijkstra 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(ν, nil) 81 -- Chapter 5. Graph Flooding via Dendrograms 83 -- 5.1. Summary of the chapter 83 -- 5.2. Introduction 84 -- 5.3. Dendrograms: reminder 86 -- 5.3.1. The structure associated with an order relation 86 -- 5.3.2. Dendrograms 87 -- 5.3.3. Stratification index and partial ultrametric distances (PUD) 88 -- 5.4. The hierarchy of lake zones 89 -- 5.4.1. The lake zones of an edge-weighted graph G(nil, η) 89 -- 5.4.2. The hierarchy of lake zones, i.e. the closed balls of χ 92 -- 5.4.3. Representing of hierarchy of lake zones 94 -- 5.5. The law of communicating vessels 98 -- 5.5.1. The flooding levels in connected subgraphs and closed balls 99. 5.6. Dominated flooding on the dendrogram of lake zones 100 -- 5.6.1. Notations 100 -- 5.6.2. Incidence of the ceiling function on the dendrogram flooding levels 100 -- 5.6.3. Finding the flooding level of a leaf 102 -- 5.6.4. Parallel processing for flooding the dendrogram 105 -- 5.6.5. Strategies for flooding the dendrogram of lake zones 106 -- 5.7. Constructing and flooding a binary dendrogram 111 -- 5.7.1. Two dendrograms representing the same hierarchy 111 -- 5.7.2. Constructing a binary dendrogram representing a hierarchy 112 -- 5.7.3. Flooding a binary dendrogram 113 -- 5.8. A derived algorithm for dominated flooding 113 -- 5.8.1. Algorithm “ancestor-flood without constructing the dendrogram” 117 -- 5.8.2. Illustration 117 -- Part 2. Modeling a Real Hydrographic Basin 119 -- Chapter 6. The Hydrographic Basin of a Digital Elevation Model 121 -- 6.1. Summary of the chapter 121 -- 6.2. Preprocessing the digital elevation model 121 -- 6.2.1. Suppressing the spurious regional minima 121 -- 6.2.2. Creating an ∞ − steep digraph 123 -- 6.2.3. Local pruning for extracting marked rivers 126 -- 6.2.4. Extracting all rivers 128 -- 6.2.5. Labeling sources and rivers 129 -- 6.2.6. Detection of crest lines 131 -- 6.2.7. Detecting the upstream of sources 132 -- 6.2.8. Analyzing the tree structure of rivers 133 -- 6.2.9. Constructing the catchment zones of riverlets 137 -- Part 3. Watershed Partitions 139 -- Chapter 7. Minimum Spanning Forests and Watershed Partitions 141 -- 7.1. Summary of the chapter 141 -- 7.2. Flooding distance, minimum spanning trees and forests 142 -- 7.2.1. Flooding distances 142 -- 7.2.2. Flooding distance on the minimum spanning tree of the graph G(nil, η) 143 -- 7.2.3. Characterizing the MST 145 -- 7.3. Minimum spanning forests rooted in markers 146 -- 7.3.1. Constructing the minimum spanning forest 147 -- 7.3.2. Converting the minimum spanning forest into a minimum spanning tree 149 -- 7.4. Watershed partitions of weighted graphs 150. 7.4.1. Catchment basins and watershed partitions 150 -- 7.4.2. Flowing paths and catchment basins 151 -- 7.5. Minimum spanning forests rooted in the regional minima 151 -- 7.5.1. A minimum spanning forest corresponds to each watershed partition 151 -- 7.5.2. Inversely, each watershed partition spans a minimum spanning forest 154 -- 7.5.3. A rather unexpected watershed partition 156 -- 7.6. A manifold of different watershed partitions 159 -- 7.6.1. Catchment zones and catchment basins 159 -- 7.7. Reducing the number of watershed partitions 160 -- 7.7.1. Minimum spanning forests of k - steep or ∞ − steep graphs 163 -- 7.7.2. The waterfall hierarchy 168 -- 7.7.3. Usefulness of the waterfall hierarchy 171 -- Chapter 8. Marker-based Segmentation 175 -- 8.1. Dominated flooding and minimum spanning forests 177 -- 8.1.1. Dominated flooding 177 -- 8.1.2. Minimum spanning forests 177 -- 8.1.3. Illustration 178 -- 8.1.4. Minimum spanning forests and dominated flooding 179 -- 8.2. Constructing a minimum spanning forest rooted in the markers 183 -- 8.2.1. Algorithms for constructing a minimum spanning forest 183 -- 8.2.2. Increasing the selectiveness of Prim’s algorithm 186 -- 8.2.3. Marker-based segmentation of node-weighted graphs 187 -- 8.2.4. Derived algorithms 190 -- 8.3. Marker-based segmentation after flooding the graph 194 -- 8.3.1. Segmenting the dominated flooding of a graph 194 -- 8.3.2. The case of an edge-weighted graph 194 -- 8.3.3. Constructing a k - steep or ∞ − steep watershed partition for a node-weighted graph G(ν, nil) 200 -- 8.4. Directly constructing a marker-based ∞ − steep watershed partition with the core expanding algorithm 201 -- 8.5. The early days of marker-based segmentation 202 -- 8.5.1. The level-by-level construction of a watershed 203 -- 8.6. A two scale marker-based segmentation 205 -- 8.7. Instant marker-based segmentation 205 -- 8.7.1. Why and when we need instant marker-based segmentation 205 -- 8.7.2. The reef and cascade distance 206. 8.7.3. Computing the reef and cascade distance for all pairs of nodes in G(nil, η) 209 -- 8.7.4. Computing the smallest reef and cascade distances between all couples of nodes in a graph 212 -- Conclusion 217 -- Appendix 227 -- References 239 -- Index 241. |
| Altri titoli varianti | Flooding and marker-based segmentation on node- or edge-weighted graphs |
| Record Nr. | UNINA-9910538499703321 |
|
Meyer Fernand <1952->
|
||
| London : , : ISTE, Ltd. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topographical tools for filtering and segmentation . 2 Flooding and marker-based segmentation on node- or edge-weighted graphs / / Fernand Meyer
| Topographical tools for filtering and segmentation . 2 Flooding and marker-based segmentation on node- or edge-weighted graphs / / Fernand Meyer |
| Autore | Meyer Fernand <1952-> |
| Pubbl/distr/stampa | London : , : ISTE, Ltd. |
| Descrizione fisica | 1 online resource (289 pages) |
| Disciplina | 551.4 |
| Collana |
Digital signal and image processing series
THEi Wiley ebooks. |
| Soggetto topico |
Relief models
Topographical drawing |
| ISBN |
1-119-57515-X
1-119-57513-3 1-119-57512-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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, η] 22 -- 1.5.3. Starting from a node-weighted graph G[ν, 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, η] 27 -- 2.2.2. n-flooding of graphs G[ν, nil] 28 -- 2.3. Regional minimum lakes and full lakes 29 -- 2.3.1. e-floodings of graphs G[nil, η] 29 -- 2.3.2. n-floodings of graphs G[ν, nil] 30 -- 2.4. Coherence between the definitions of lakes in G[ν, nil] and in G[nil, δenν] 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, η] 38.
3.3.2. The regional minima of dominated n-flooding in node-weighted graphs G[ν, 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, η] 43 -- 3.4.2. The case of node-weighted graphs G[ν, 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 Moore-Dijkstra 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(ν, nil) 81 -- Chapter 5. Graph Flooding via Dendrograms 83 -- 5.1. Summary of the chapter 83 -- 5.2. Introduction 84 -- 5.3. Dendrograms: reminder 86 -- 5.3.1. The structure associated with an order relation 86 -- 5.3.2. Dendrograms 87 -- 5.3.3. Stratification index and partial ultrametric distances (PUD) 88 -- 5.4. The hierarchy of lake zones 89 -- 5.4.1. The lake zones of an edge-weighted graph G(nil, η) 89 -- 5.4.2. The hierarchy of lake zones, i.e. the closed balls of χ 92 -- 5.4.3. Representing of hierarchy of lake zones 94 -- 5.5. The law of communicating vessels 98 -- 5.5.1. The flooding levels in connected subgraphs and closed balls 99. 5.6. Dominated flooding on the dendrogram of lake zones 100 -- 5.6.1. Notations 100 -- 5.6.2. Incidence of the ceiling function on the dendrogram flooding levels 100 -- 5.6.3. Finding the flooding level of a leaf 102 -- 5.6.4. Parallel processing for flooding the dendrogram 105 -- 5.6.5. Strategies for flooding the dendrogram of lake zones 106 -- 5.7. Constructing and flooding a binary dendrogram 111 -- 5.7.1. Two dendrograms representing the same hierarchy 111 -- 5.7.2. Constructing a binary dendrogram representing a hierarchy 112 -- 5.7.3. Flooding a binary dendrogram 113 -- 5.8. A derived algorithm for dominated flooding 113 -- 5.8.1. Algorithm “ancestor-flood without constructing the dendrogram” 117 -- 5.8.2. Illustration 117 -- Part 2. Modeling a Real Hydrographic Basin 119 -- Chapter 6. The Hydrographic Basin of a Digital Elevation Model 121 -- 6.1. Summary of the chapter 121 -- 6.2. Preprocessing the digital elevation model 121 -- 6.2.1. Suppressing the spurious regional minima 121 -- 6.2.2. Creating an ∞ − steep digraph 123 -- 6.2.3. Local pruning for extracting marked rivers 126 -- 6.2.4. Extracting all rivers 128 -- 6.2.5. Labeling sources and rivers 129 -- 6.2.6. Detection of crest lines 131 -- 6.2.7. Detecting the upstream of sources 132 -- 6.2.8. Analyzing the tree structure of rivers 133 -- 6.2.9. Constructing the catchment zones of riverlets 137 -- Part 3. Watershed Partitions 139 -- Chapter 7. Minimum Spanning Forests and Watershed Partitions 141 -- 7.1. Summary of the chapter 141 -- 7.2. Flooding distance, minimum spanning trees and forests 142 -- 7.2.1. Flooding distances 142 -- 7.2.2. Flooding distance on the minimum spanning tree of the graph G(nil, η) 143 -- 7.2.3. Characterizing the MST 145 -- 7.3. Minimum spanning forests rooted in markers 146 -- 7.3.1. Constructing the minimum spanning forest 147 -- 7.3.2. Converting the minimum spanning forest into a minimum spanning tree 149 -- 7.4. Watershed partitions of weighted graphs 150. 7.4.1. Catchment basins and watershed partitions 150 -- 7.4.2. Flowing paths and catchment basins 151 -- 7.5. Minimum spanning forests rooted in the regional minima 151 -- 7.5.1. A minimum spanning forest corresponds to each watershed partition 151 -- 7.5.2. Inversely, each watershed partition spans a minimum spanning forest 154 -- 7.5.3. A rather unexpected watershed partition 156 -- 7.6. A manifold of different watershed partitions 159 -- 7.6.1. Catchment zones and catchment basins 159 -- 7.7. Reducing the number of watershed partitions 160 -- 7.7.1. Minimum spanning forests of k - steep or ∞ − steep graphs 163 -- 7.7.2. The waterfall hierarchy 168 -- 7.7.3. Usefulness of the waterfall hierarchy 171 -- Chapter 8. Marker-based Segmentation 175 -- 8.1. Dominated flooding and minimum spanning forests 177 -- 8.1.1. Dominated flooding 177 -- 8.1.2. Minimum spanning forests 177 -- 8.1.3. Illustration 178 -- 8.1.4. Minimum spanning forests and dominated flooding 179 -- 8.2. Constructing a minimum spanning forest rooted in the markers 183 -- 8.2.1. Algorithms for constructing a minimum spanning forest 183 -- 8.2.2. Increasing the selectiveness of Prim’s algorithm 186 -- 8.2.3. Marker-based segmentation of node-weighted graphs 187 -- 8.2.4. Derived algorithms 190 -- 8.3. Marker-based segmentation after flooding the graph 194 -- 8.3.1. Segmenting the dominated flooding of a graph 194 -- 8.3.2. The case of an edge-weighted graph 194 -- 8.3.3. Constructing a k - steep or ∞ − steep watershed partition for a node-weighted graph G(ν, nil) 200 -- 8.4. Directly constructing a marker-based ∞ − steep watershed partition with the core expanding algorithm 201 -- 8.5. The early days of marker-based segmentation 202 -- 8.5.1. The level-by-level construction of a watershed 203 -- 8.6. A two scale marker-based segmentation 205 -- 8.7. Instant marker-based segmentation 205 -- 8.7.1. Why and when we need instant marker-based segmentation 205 -- 8.7.2. The reef and cascade distance 206. 8.7.3. Computing the reef and cascade distance for all pairs of nodes in G(nil, η) 209 -- 8.7.4. Computing the smallest reef and cascade distances between all couples of nodes in a graph 212 -- Conclusion 217 -- Appendix 227 -- References 239 -- Index 241. |
| Altri titoli varianti | Flooding and marker-based segmentation on node- or edge-weighted graphs |
| Record Nr. | UNINA-9910808285503321 |
|
Meyer Fernand <1952->
|
||
| London : , : ISTE, Ltd. | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||