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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. . 1 Watersheds on node- or edge-weighted graphs / / Fernand Meyer
| Topographical tools for filtering and segmentation. . 1 Watersheds 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 | 551.41 |
| Soggetto topico |
Relief models
Topographical drawing |
| ISBN |
1-119-57955-4
1-119-57951-1 1-119-57954-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Notations xiii -- Introduction xxvii -- Part 1. Getting Started 1 -- Chapter 1. A Primer to Flooding, Razing and Watersheds 3 -- 1.1. Topographic reliefs and topographic features 3 -- 1.1.1. Images seen as topographic reliefs and inversely 3 -- 1.1.2. Topographic features 5 -- 1.1.3. Modeling a topographic relief as a weighted graph 8 -- 1.2. Flooding, razing and morphological filters 10 -- 1.2.1. The principle of duality 10 -- 1.2.2. Dominated flooding and razing 10 -- 1.2.3. Flooding, razing and catchment zones of a topographic relief 16 -- 1.3. Catchment zones of flooded surfaces 18 -- 1.3.1. Filtering and segmenting 18 -- 1.3.2. Reducing the oversegmentation with markers 19 -- 1.4. The waterfall hierarchy 26 -- 1.4.1. Overflows between catchment basins 26 -- 1.5. Size-driven hierarchies 28 -- 1.6. Separating overlapping particles in n dimensions 31 -- 1.7. Catchment zones and lakes of region neighborhood graphs 33 -- 1.8. Conclusion 37 -- Chapter 2. Watersheds and Flooding: a Segmentation Golden Braid 39 -- 2.1. Watersheds, offsprings and parallel branches 40 -- 2.2. Flooding and connected operators 43 -- 2.3. Connected operators and hierarchies 45 -- 2.4. Hierarchical segmentation: extinction values 47 -- Chapter 3. Mathematical Notions 49 -- 3.1. Summary of the chapter 49 -- 3.2. Complete lattices 49 -- 3.2.1. Partial order and partially ordered sets 49 -- 3.2.2. Upper and lower bounds 50 -- 3.2.3. Complete lattices 50 -- 3.2.4. Dyadic relations on a complete lattice 51 -- 3.3. Operators between complete lattices 51 -- 3.3.1. Definition of an operator 51 -- 3.3.2. Properties of the operators 52 -- 3.3.3. Erosion and dilation 52 -- 3.3.4. Opening and closing 53 -- 3.4. The adjunction: a cornerstone of mathematical morphology 53 -- 3.4.1. Adjoint erosions and dilations 53 -- 3.4.2. Increasingness 53 -- 3.4.3. Unicity 53 -- 3.4.4. Composition 54 -- 3.4.5. Dual operators 54 -- 3.5. Openings and closings 54 -- 3.5.1. Definitions 54 -- 3.5.2. Elements with the same erosion or the same dilation 55.
3.5.3. The invariants of an opening or a closing 55 -- 3.6. Complete lattices of functions 55 -- 3.6.1. Definitions 55 -- 3.6.2. Infimum and supremum 56 -- Part 2. The Topography of Weighted Graphs 57 -- Chapter 4. Weighted Graphs 59 -- 4.1. Summary of the chapter 59 -- 4.2. Reminders on graphs 60 -- 4.2.1. Directed and undirected graphs 60 -- 4.3. Weight distributions on the nodes or edges of a graph 62 -- 4.3.1. Duality 63 -- 4.3.2. Erosions and dilations, openings, closings 63 -- 4.3.3. Labels 66 -- 4.4. Exploring the topography of graphs by following a drop of water 66 -- 4.5. Node-weighted graphs 67 -- 4.5.1. Flat zones and regional minima 67 -- 4.5.2. Flowing paths and catchment zones 67 -- 4.6. Edge-weighted graphs 69 -- 4.6.1. Flat zones and regional minima 69 -- 4.6.2. Flowing paths and catchment zones 69 -- 4.6.3. Even zones and regional minima 71 -- 4.7. Comparing the topography of node-weighted graphs and edge-weighted graphs 72 -- Chapter 5. Flowing Graphs 73 -- 5.1. Summary of the chapter 73 -- 5.2. Towards a convergence between node- and edge-weighted graphs 74 -- 5.2.1. The flowing edges in a node-weighted graph G(ν, nil) 74 -- 5.2.2. The flowing edges in an edge-weighted graph G(nil, η) 75 -- 5.2.3. Flowing graphs 76 -- 5.3. The flowing adjunction 76 -- 5.4. Flowing edges under closer scrutiny 77 -- 5.4.1. Relations between the flowing edges of G(ν, nil) and G(nil, δenν) 77 -- 5.4.2. Relations between the flowing edges of G(nil, η) and G(εneη, nil) 78 -- 5.4.3. Chaining the inclusions between flowing edges 78 -- 5.4.4. Criteria characterizing flowing graphs 79 -- 5.4.5. Transforming a node- or edge-weighted graph into a flowing graph 81 -- 5.4.6. The invariance domains of γe and ϕn 83 -- 5.4.7. Particular flowing graphs 87 -- 5.5. Illustration as a hydrographic model 88 -- 5.5.1. A hydrographic model of tanks and pipes 88 -- 5.5.2. Associating an “edge unstable” tank network with an arbitrary node-weighted graph G(ν, nil) 90. 5.5.3. Associating a “node unstable” tank network with an arbitrary edge-weighted graph G(nil, η) 91 -- 5.5.4. Chaining the operations 92 -- Chapter 6. The Topography of Digraphs 97 -- 6.1. Summary of the chapter 97 -- 6.1.1. General digraphs 98 -- 6.1.2. Digraphs without perpetuum mobile configurations 98 -- 6.2. Status report 98 -- 6.2.1. Case of node-weighted graphs 99 -- 6.2.2. Case of edge-weighted graphs 99 -- 6.3. The topography of unweighted digraphs 100 -- 6.3.1. Notations 100 -- 6.3.2. Smooth zones, dead ends, flat zones and black holes of digraphs 101 -- 6.4. The topography of gravitational digraphs 105 -- 6.4.1. No “perpetuum mobile” 105 -- 6.4.2. Defining and propagating labels 107 -- 6.4.3. A dead leaves model of catchment zones 113 -- 6.4.4. Examples of gravitational graphs 122 -- 6.4.5. The topography of weighted graphs interpreted in the light of the derived digraphs 122 -- Part 3. Reducing the Overlapping of Catchment Zones 125 -- Chapter 7. Measuring the Steepness of Flowing Paths 127 -- 7.1. Summary of the chapter 127 -- 7.2. Why do the catchment zones overlap? 128 -- 7.2.1. Relation between the catchment zones and the flowing paths 128 -- 7.2.2. Comparing the steepness of flowing paths 128 -- 7.2.3. The redundancy between node and edge weights 129 -- 7.2.4. General flow digraphs 130 -- 7.3. The lexicographic pre-order relation of length k 131 -- 7.3.1. Prolonging flowing paths into paths of infinite length 131 -- 7.3.2. Comparing the steepness of two flowing paths 132 -- 7.3.3. Properties of ∞ − steep paths 134 -- Chapter 8. Pruning a Flow Digraph 137 -- 8.1. Summary of the chapter 137 -- 8.1.1. Transforming a node- or edge-weighted graph into a node-weighted flowing digraph (reminder) 137 -- 8.1.2. Global pruning 138 -- 8.1.3. Local pruning 138 -- 8.2. The pruning operator 138 -- 8.2.1. Two operators on flow digraphs 139 -- 8.2.2. Pruning by concatenating both operators 140 -- 8.2.3. Properties of pruning 142. 8.2.4. A variant of pruning 146 -- 8.2.5. Local pruning -- 8.3. Evolution of catchment zones with pruning 147 -- 8.3.1. Analyzing a digital elevation model 148 -- Chapter 9. Constructing an ∞ - steep Digraph by Flooding 155 -- 9.1. Summary of the chapter 155 -- 9.2. Characterization of ∞ − steep graphs 156 -- 9.3. The core-expanding flooding algorithm 156 -- 9.3.1. The first version of the core-expanding algorithm 157 -- 9.3.2. The second version of the core-expanding algorithm 160 -- 9.3.3. The third version of the core-expanding algorithm 164 -- 9.3.4. The last version of the core-expanding algorithm, constructing a partial ∞ − steep flowing graph 167 -- Chapter 10. Creating Steep Watershed Partitions 169 -- 10.1. Summary of the chapter 169 -- 10.2. Creating watershed partitions with the core-expanding algorithm 169 -- 10.2.1. Illustration of the HQ algorithm applied to node-weighted graphs 171 -- 10.3. Propagating labels while pruning the digraph 172 -- 10.3.1. Constructing a watershed partition during pruning 173 -- 10.4. Pruning or flooding: two ways for catchment zones to grow 176 -- Chapter 11. An Historical Intermezzo 179 -- 11.1. Watersheds: the early days 179 -- 11.1.1. The level-by-level construction of watersheds 180 -- 11.1.2. A hierarchical queue watershed algorithm 181 -- 11.2. A watershed as the SKIZ for the topographic distance 181 -- 11.2.1. The topographic distance 181 -- 11.3. Convergence into a unique algorithm of three research streams 182 -- 11.3.1. Three formulations of watershed partitions, one algorithm 182 -- 11.3.2. Discussion 183 -- Part 4. Segmenting with Dead Leaves Partitions 185 -- Chapter 12. Intermezzo: Encoding the Digraph Associated with an Image 187 -- 12.1. Summary of the theoretical developments seen so far 187 -- 12.2. Summary of the chapter 188 -- 12.3. Representing a node-weighted digraph as two images 188 -- 12.3.1. The encoding of the digraph associated with an image 188 -- 12.3.2. Operators acting on node-weighted digraphs 190. 12.4. Defining labels 192 -- 12.4.1. Operators on unweighted unlabeled digraphs 193 -- 12.4.2. Operators on labeled unweighted digraphs 194 -- 12.4.3. Operators on weighted and labeled digraphs 198 -- Chapter 13. Two Paradigms for Creating a Partition or a Partial Partition on a Graph 203 -- 13.1. Summary of the chapter 203 -- 13.2. Setting up a common stage for node- and edge-weighted graphs 203 -- 13.3. A brief tool inventory 204 -- 13.3.1. Operators making no use of the node weights 204 -- 13.3.2. Operators propagating labels 204 -- 13.3.3. Operators making use of the node weights and the graph structure 205 -- 13.4. Dead leaves tessellations versus tilings: two paradigms 205 -- 13.5. Extracting catchment zones containing a particular node 206 -- 13.5.1. Core expansion versus pruning algorithms 206 -- 13.5.2. Illustration of the pruning algorithm 207 -- 13.6. Catchment zones versus catchment basins 209 -- Chapter 14. Dead Leaves Segmentation 211 -- 14.1. Summary of the chapter 211 -- 14.2. Segmenting with a watershed 211 -- 14.2.1. Segmenting with watershed partitions 211 -- 14.2.2. A crossroad of several methods 213 -- 14.3. The evolution of a dead leaves tessellation with pruning 214 -- 14.4. Local correction of overlapping zones 217 -- 14.4.1. Pruning analysis 217 -- 14.4.2. Local pruning for reducing overlapping zones 219 -- 14.4.3. A local core-expanding algorithm for reducing overlapping zones 221 -- 14.5. Local correction of the overlapping zones on a DEM 221 -- 14.5.1. Local core-expanding algorithm for reducing overlapping zones 225 -- 14.5.2. Advantage of the two-step construction of a dead leaves tessellation 227 -- 14.6. Segmentation of some marked regions 231 -- 14.6.1. Segmenting the domain and extracting the objects of interest 232 -- 14.6.2. Extraction of the marked catchment zones and local correction of errors 233 -- Chapter 15. Propagating Segmentations 241 -- 15.1. Summary of the chapter 241 -- 15.2. Step-by-step segmentation 241 -- 15.2.1. Principle of the method 241. 15.2.2. Segmentation of blood cells 242 -- 15.2.3. Segmentation of an electronic circuit 243 -- 15.3. Marker-based segmentation 245 -- Appendix 247 -- References 259 -- Index 267. |
| Record Nr. | UNINA-9910555036703321 |
|
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 | ||
| ||
Topographical tools for filtering and segmentation. . 1 Watersheds on node- or edge-weighted graphs / / Fernand Meyer
| Topographical tools for filtering and segmentation. . 1 Watersheds on node- or edge-weighted graphs / / Fernand Meyer |
| Autore | Meyer Fernand <1952-> |
| Pubbl/distr/stampa | London, United Kingdom : , : ISTE, Ltd., , [2019] |
| Descrizione fisica | 1 online resource |
| Disciplina | 551.41 |
| Soggetto topico |
Relief models
Topographical drawing |
| ISBN |
1-119-57955-4
1-119-57951-1 1-119-57954-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Notations xiii -- Introduction xxvii -- Part 1. Getting Started 1 -- Chapter 1. A Primer to Flooding, Razing and Watersheds 3 -- 1.1. Topographic reliefs and topographic features 3 -- 1.1.1. Images seen as topographic reliefs and inversely 3 -- 1.1.2. Topographic features 5 -- 1.1.3. Modeling a topographic relief as a weighted graph 8 -- 1.2. Flooding, razing and morphological filters 10 -- 1.2.1. The principle of duality 10 -- 1.2.2. Dominated flooding and razing 10 -- 1.2.3. Flooding, razing and catchment zones of a topographic relief 16 -- 1.3. Catchment zones of flooded surfaces 18 -- 1.3.1. Filtering and segmenting 18 -- 1.3.2. Reducing the oversegmentation with markers 19 -- 1.4. The waterfall hierarchy 26 -- 1.4.1. Overflows between catchment basins 26 -- 1.5. Size-driven hierarchies 28 -- 1.6. Separating overlapping particles in n dimensions 31 -- 1.7. Catchment zones and lakes of region neighborhood graphs 33 -- 1.8. Conclusion 37 -- Chapter 2. Watersheds and Flooding: a Segmentation Golden Braid 39 -- 2.1. Watersheds, offsprings and parallel branches 40 -- 2.2. Flooding and connected operators 43 -- 2.3. Connected operators and hierarchies 45 -- 2.4. Hierarchical segmentation: extinction values 47 -- Chapter 3. Mathematical Notions 49 -- 3.1. Summary of the chapter 49 -- 3.2. Complete lattices 49 -- 3.2.1. Partial order and partially ordered sets 49 -- 3.2.2. Upper and lower bounds 50 -- 3.2.3. Complete lattices 50 -- 3.2.4. Dyadic relations on a complete lattice 51 -- 3.3. Operators between complete lattices 51 -- 3.3.1. Definition of an operator 51 -- 3.3.2. Properties of the operators 52 -- 3.3.3. Erosion and dilation 52 -- 3.3.4. Opening and closing 53 -- 3.4. The adjunction: a cornerstone of mathematical morphology 53 -- 3.4.1. Adjoint erosions and dilations 53 -- 3.4.2. Increasingness 53 -- 3.4.3. Unicity 53 -- 3.4.4. Composition 54 -- 3.4.5. Dual operators 54 -- 3.5. Openings and closings 54 -- 3.5.1. Definitions 54 -- 3.5.2. Elements with the same erosion or the same dilation 55.
3.5.3. The invariants of an opening or a closing 55 -- 3.6. Complete lattices of functions 55 -- 3.6.1. Definitions 55 -- 3.6.2. Infimum and supremum 56 -- Part 2. The Topography of Weighted Graphs 57 -- Chapter 4. Weighted Graphs 59 -- 4.1. Summary of the chapter 59 -- 4.2. Reminders on graphs 60 -- 4.2.1. Directed and undirected graphs 60 -- 4.3. Weight distributions on the nodes or edges of a graph 62 -- 4.3.1. Duality 63 -- 4.3.2. Erosions and dilations, openings, closings 63 -- 4.3.3. Labels 66 -- 4.4. Exploring the topography of graphs by following a drop of water 66 -- 4.5. Node-weighted graphs 67 -- 4.5.1. Flat zones and regional minima 67 -- 4.5.2. Flowing paths and catchment zones 67 -- 4.6. Edge-weighted graphs 69 -- 4.6.1. Flat zones and regional minima 69 -- 4.6.2. Flowing paths and catchment zones 69 -- 4.6.3. Even zones and regional minima 71 -- 4.7. Comparing the topography of node-weighted graphs and edge-weighted graphs 72 -- Chapter 5. Flowing Graphs 73 -- 5.1. Summary of the chapter 73 -- 5.2. Towards a convergence between node- and edge-weighted graphs 74 -- 5.2.1. The flowing edges in a node-weighted graph G(ν, nil) 74 -- 5.2.2. The flowing edges in an edge-weighted graph G(nil, η) 75 -- 5.2.3. Flowing graphs 76 -- 5.3. The flowing adjunction 76 -- 5.4. Flowing edges under closer scrutiny 77 -- 5.4.1. Relations between the flowing edges of G(ν, nil) and G(nil, δenν) 77 -- 5.4.2. Relations between the flowing edges of G(nil, η) and G(εneη, nil) 78 -- 5.4.3. Chaining the inclusions between flowing edges 78 -- 5.4.4. Criteria characterizing flowing graphs 79 -- 5.4.5. Transforming a node- or edge-weighted graph into a flowing graph 81 -- 5.4.6. The invariance domains of γe and ϕn 83 -- 5.4.7. Particular flowing graphs 87 -- 5.5. Illustration as a hydrographic model 88 -- 5.5.1. A hydrographic model of tanks and pipes 88 -- 5.5.2. Associating an “edge unstable” tank network with an arbitrary node-weighted graph G(ν, nil) 90. 5.5.3. Associating a “node unstable” tank network with an arbitrary edge-weighted graph G(nil, η) 91 -- 5.5.4. Chaining the operations 92 -- Chapter 6. The Topography of Digraphs 97 -- 6.1. Summary of the chapter 97 -- 6.1.1. General digraphs 98 -- 6.1.2. Digraphs without perpetuum mobile configurations 98 -- 6.2. Status report 98 -- 6.2.1. Case of node-weighted graphs 99 -- 6.2.2. Case of edge-weighted graphs 99 -- 6.3. The topography of unweighted digraphs 100 -- 6.3.1. Notations 100 -- 6.3.2. Smooth zones, dead ends, flat zones and black holes of digraphs 101 -- 6.4. The topography of gravitational digraphs 105 -- 6.4.1. No “perpetuum mobile” 105 -- 6.4.2. Defining and propagating labels 107 -- 6.4.3. A dead leaves model of catchment zones 113 -- 6.4.4. Examples of gravitational graphs 122 -- 6.4.5. The topography of weighted graphs interpreted in the light of the derived digraphs 122 -- Part 3. Reducing the Overlapping of Catchment Zones 125 -- Chapter 7. Measuring the Steepness of Flowing Paths 127 -- 7.1. Summary of the chapter 127 -- 7.2. Why do the catchment zones overlap? 128 -- 7.2.1. Relation between the catchment zones and the flowing paths 128 -- 7.2.2. Comparing the steepness of flowing paths 128 -- 7.2.3. The redundancy between node and edge weights 129 -- 7.2.4. General flow digraphs 130 -- 7.3. The lexicographic pre-order relation of length k 131 -- 7.3.1. Prolonging flowing paths into paths of infinite length 131 -- 7.3.2. Comparing the steepness of two flowing paths 132 -- 7.3.3. Properties of ∞ − steep paths 134 -- Chapter 8. Pruning a Flow Digraph 137 -- 8.1. Summary of the chapter 137 -- 8.1.1. Transforming a node- or edge-weighted graph into a node-weighted flowing digraph (reminder) 137 -- 8.1.2. Global pruning 138 -- 8.1.3. Local pruning 138 -- 8.2. The pruning operator 138 -- 8.2.1. Two operators on flow digraphs 139 -- 8.2.2. Pruning by concatenating both operators 140 -- 8.2.3. Properties of pruning 142. 8.2.4. A variant of pruning 146 -- 8.2.5. Local pruning -- 8.3. Evolution of catchment zones with pruning 147 -- 8.3.1. Analyzing a digital elevation model 148 -- Chapter 9. Constructing an ∞ - steep Digraph by Flooding 155 -- 9.1. Summary of the chapter 155 -- 9.2. Characterization of ∞ − steep graphs 156 -- 9.3. The core-expanding flooding algorithm 156 -- 9.3.1. The first version of the core-expanding algorithm 157 -- 9.3.2. The second version of the core-expanding algorithm 160 -- 9.3.3. The third version of the core-expanding algorithm 164 -- 9.3.4. The last version of the core-expanding algorithm, constructing a partial ∞ − steep flowing graph 167 -- Chapter 10. Creating Steep Watershed Partitions 169 -- 10.1. Summary of the chapter 169 -- 10.2. Creating watershed partitions with the core-expanding algorithm 169 -- 10.2.1. Illustration of the HQ algorithm applied to node-weighted graphs 171 -- 10.3. Propagating labels while pruning the digraph 172 -- 10.3.1. Constructing a watershed partition during pruning 173 -- 10.4. Pruning or flooding: two ways for catchment zones to grow 176 -- Chapter 11. An Historical Intermezzo 179 -- 11.1. Watersheds: the early days 179 -- 11.1.1. The level-by-level construction of watersheds 180 -- 11.1.2. A hierarchical queue watershed algorithm 181 -- 11.2. A watershed as the SKIZ for the topographic distance 181 -- 11.2.1. The topographic distance 181 -- 11.3. Convergence into a unique algorithm of three research streams 182 -- 11.3.1. Three formulations of watershed partitions, one algorithm 182 -- 11.3.2. Discussion 183 -- Part 4. Segmenting with Dead Leaves Partitions 185 -- Chapter 12. Intermezzo: Encoding the Digraph Associated with an Image 187 -- 12.1. Summary of the theoretical developments seen so far 187 -- 12.2. Summary of the chapter 188 -- 12.3. Representing a node-weighted digraph as two images 188 -- 12.3.1. The encoding of the digraph associated with an image 188 -- 12.3.2. Operators acting on node-weighted digraphs 190. 12.4. Defining labels 192 -- 12.4.1. Operators on unweighted unlabeled digraphs 193 -- 12.4.2. Operators on labeled unweighted digraphs 194 -- 12.4.3. Operators on weighted and labeled digraphs 198 -- Chapter 13. Two Paradigms for Creating a Partition or a Partial Partition on a Graph 203 -- 13.1. Summary of the chapter 203 -- 13.2. Setting up a common stage for node- and edge-weighted graphs 203 -- 13.3. A brief tool inventory 204 -- 13.3.1. Operators making no use of the node weights 204 -- 13.3.2. Operators propagating labels 204 -- 13.3.3. Operators making use of the node weights and the graph structure 205 -- 13.4. Dead leaves tessellations versus tilings: two paradigms 205 -- 13.5. Extracting catchment zones containing a particular node 206 -- 13.5.1. Core expansion versus pruning algorithms 206 -- 13.5.2. Illustration of the pruning algorithm 207 -- 13.6. Catchment zones versus catchment basins 209 -- Chapter 14. Dead Leaves Segmentation 211 -- 14.1. Summary of the chapter 211 -- 14.2. Segmenting with a watershed 211 -- 14.2.1. Segmenting with watershed partitions 211 -- 14.2.2. A crossroad of several methods 213 -- 14.3. The evolution of a dead leaves tessellation with pruning 214 -- 14.4. Local correction of overlapping zones 217 -- 14.4.1. Pruning analysis 217 -- 14.4.2. Local pruning for reducing overlapping zones 219 -- 14.4.3. A local core-expanding algorithm for reducing overlapping zones 221 -- 14.5. Local correction of the overlapping zones on a DEM 221 -- 14.5.1. Local core-expanding algorithm for reducing overlapping zones 225 -- 14.5.2. Advantage of the two-step construction of a dead leaves tessellation 227 -- 14.6. Segmentation of some marked regions 231 -- 14.6.1. Segmenting the domain and extracting the objects of interest 232 -- 14.6.2. Extraction of the marked catchment zones and local correction of errors 233 -- Chapter 15. Propagating Segmentations 241 -- 15.1. Summary of the chapter 241 -- 15.2. Step-by-step segmentation 241 -- 15.2.1. Principle of the method 241. 15.2.2. Segmentation of blood cells 242 -- 15.2.3. Segmentation of an electronic circuit 243 -- 15.3. Marker-based segmentation 245 -- Appendix 247 -- References 259 -- Index 267. |
| Record Nr. | UNINA-9910829819803321 |
|
Meyer Fernand <1952->
|
||
| London, United Kingdom : , : ISTE, Ltd., , [2019] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||