{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":28,"n_cols":5,"rows_kept":28,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[6,2,6,3],[9,2,9,3],[10,2,10,3],[12,2,12,3],[13,2,13,3],[15,2,15,3],[16,2,16,3],[19,2,19,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9910538499703321"]
[null,null,"Autore",null,"Meyer Fernand <1952->"]
[null,null,"Titolo",null,"Topographical tools for filtering and segmentation . 2 Flooding and marker-based segmentation on node- or edge-weighted graphs / / Fernand Meyer"]
[null,null,"Pubbl/distr/stampa",null,"London : , : ISTE, Ltd."]
[{"$nulls":4},"Hoboken, NJ : , : Wiley, , 2019"]
[{"$nulls":4},"[Piscataway, New Jersey] : , : IEEE Xplore, , [2019]"]
[null,null,"ISBN",null,"1-119-57515-X"]
[{"$nulls":4},"1-119-57513-3"]
[{"$nulls":4},"1-119-57512-5"]
[null,null,"Descrizione fisica",null,"1 online resource (289 pages)"]
[null,null,"Collana",null,"Digital signal and image processing series"]
[{"$nulls":4},"THEi Wiley ebooks."]
[null,null,"Disciplina",null,"551.4"]
[null,null,"Soggetti",null,"Relief models"]
[{"$nulls":4},"Topographical drawing"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"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, &eta;] 22 -- 1.5.3. Starting from a node-weighted graph G[&nu;, 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, &eta;] 27 -- 2.2.2. n-flooding of "]
[{"$nulls":4},"graphs G[&nu;, nil] 28 -- 2.3. Regional minimum lakes and full lakes 29 -- 2.3.1. e-floodings of graphs G[nil, &eta;] 29 -- 2.3.2. n-floodings of graphs G[&nu;, nil] 30 -- 2.4. Coherence between the definitions of lakes in G[&nu;, nil] and in G[nil, &delta;en&nu;] 31 -- Chapter 3. Among all Possible Floodings, Choosing One 33 -- 3.1. Summary of the chapter 33 -- 3.2. Various mechanisms for selecting a particular flooding 34 -- 3.2.1. Dominated flooding in node- and edge-weighted graphs 34 -- 3.2.2. Dominated flooding in node- and edge-weighted graphs 36 -- 3.2.3. Dominated flooding as a function of the ceiling function 37 -- 3.3. The topography of dominated flooding 37 -- 3.3.1. The regional minima of dominated flooding in an edge-weighted graph G[nil, &eta;] 38."]
[{"$nulls":4},"3.3.2. The regional minima of dominated n-flooding in node-weighted graphs G[&nu;, 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, &eta;] 43 -- 3.4.2. The case of node-weighted graphs G[&nu;, nil] 44 -- 3.4.3. Software or hardware implementation of Berge&rsquo;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 G&Acirc; 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(&nu;, 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, &eta;) 89 -- 5.4.2. The hierarchy of lake zones, i.e. the closed balls of &chi; 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."]
[{"$nulls":4},"5.6. Dominated flooding on the dendrogram of lake zones 100 -- 5.6.1. Notations 100 -- 5.6.2. Incidence of the ceiling function on the dendrogram flooding levels 100 -- 5.6.3. Finding the flooding level of a leaf 102 -- 5.6.4. Parallel processing for flooding the dendrogram 105 -- 5.6.5. Strategies for flooding the dendrogram of lake zones 106 -- 5.7. Constructing and flooding a binary dendrogram 111 -- 5.7.1. Two dendrograms representing the same hierarchy 111 -- 5.7.2. Constructing a binary dendrogram representing a hierarchy 112 -- 5.7.3. Flooding a binary dendrogram 113 -- 5.8. A derived algorithm for dominated flooding 113 -- 5.8.1. Algorithm &ldquo;ancestor-flood without constructing the dendrogram&rdquo; 117 -- 5.8.2. Illustration 117 -- Part 2. Modeling a Real Hydrographic Basin 119 -- Chapter 6. The Hydrographic Basin of a Digital Elevation Model 121 -- 6.1. Summary of the chapter 121 -- 6.2. Preprocessing the digital elevation model 121 -- 6.2.1. Suppressing the spurious regional minima 121 -- "]
[{"$nulls":4},"6.2.2. Creating an &infin; &minus; 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, &eta;) 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."]
[{"$nulls":4},"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 &infin; &minus; 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&rsquo;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 &infin; &minus; steep watershed partition for a node-weighted graph G(&nu;, nil) 200 -- 8.4. Directly constructing a marker-based &infin; &minus; 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."]
[{"$nulls":4},"8.7.3. Computing the reef and cascade distance for all pairs of nodes in G(nil, &eta;) 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."]
[null,null,null,"Sommario/riassunto","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 "]
[{"$nulls":4},"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. '"]