Ranking the vertices of a weighted digraph using the length of forward arcs

Networks ◽  
1983 ◽  
Vol 13 (1) ◽  
pp. 143-151 ◽  
Author(s):  
Mikio Kano ◽  
Akio Sakamoto
Keyword(s):  
Weighted Digraph

scholarly journals An Efficient Hierarchical Layered Graph Approach for Multi-Region Segmentation

2019 ◽  
Author(s):  
Leissi M. Castañeda Leon ◽  
Krzysztof Chris Ciesielski ◽  
Paulo A. Vechiatto Miranda
Keyword(s):  
State Of The Art ◽  
Region Segmentation ◽  
Hierarchical Segmentation ◽  
Image Objects ◽  
Hierarchical Relations ◽  
Flow Algorithm ◽  
Segmentation Of Images ◽  
High Level ◽  
Layered Graph ◽  
Weighted Digraph

We proposed a novel efficient seed-based method for the multiple region segmentation of images based on graphs, named Hierarchical Layered Oriented Image Foresting Transform (HLOIFT). It uses a tree of the relations between the image objects, represented by a node. Each tree node may contain different individual high-level priors and defines a weighted digraph, named as layer. The layer graphs are then integrated into a hierarchical graph, considering the hierarchical relations of inclusion and exclusion. A single energy optimization is performed in the hierarchical layered weighted digraph leading to globally optimal results satisfying all the high-level priors. The experimental evaluations of HLOIFT and its extensions, on medical, natural and synthetic images, indicate promising results comparable to the state-of-the-art methods, but with lower computational complexity. Compared to hierarchical segmentation by the min-cut/max-flow algorithm, our approach is less restrictive, leading to globally optimal results in more general scenarios, and has a better running time.

scholarly journals A decentralized algorithm for balancing a strongly connected weighted digraph

2013 ◽  
Author(s):  
Attilio Priolo ◽  
Andrea Gasparri ◽  
Eduardo Montijano ◽  
Carlos Sagues
Keyword(s):  
Strongly Connected ◽  
Weighted Digraph

Optimal subgraphs in a weighted digraph

Cybernetics ◽  
1981 ◽  
Vol 17 (2) ◽  
pp. 172-176
Author(s):  
D. D. Lozovanu
Keyword(s):  
Weighted Digraph

Efficient Hierarchical Multi-Object Segmentation in Layered Graphs

2021 ◽  
Vol 5 (1) ◽  
pp. 21-42
Author(s):  
Leissi M.C. Leon ◽  
Krzysztof C. Ciesielski ◽  
Paulo A.V. Miranda
Keyword(s):  
Object Segmentation ◽  
Structural Information ◽  
Hierarchical Segmentation ◽  
Image Objects ◽  
Hierarchical Relations ◽  
Flow Algorithm ◽  
Segmentation Of Images ◽  
High Level ◽  
Min Cut ◽  
Weighted Digraph

Abstract We propose a novel efficient seed-based method for the multi-object segmentation of images based on graphs, named Hierarchical Layered Oriented Image Foresting Transform (HLOIFT). It uses a tree of the relations between the image objects, with each node in the tree representing an object. Each tree node may contain different individual high-level priors of its corresponding object and defines a weighted digraph, named as layer. The layer graphs are then integrated into a hierarchical graph, considering the hierarchical relations of inclusion and exclusion. A single energy optimization is performed in the hierarchical layered weighted digraph leading to globally optimal results satisfying all the high-level priors. The experimental evaluations of HLOIFT, on medical, natural, and synthetic images, indicate promising results comparable to the related baseline methods that include structural information, but with lower computational complexity. Compared to the hierarchical segmentation by the min-cut/max-flow algorithm, our approach is less restrictive, leading to globally optimal results in more general scenarios, and has a better running time.

scholarly journals Chains of three-dimensional evolution algebras: A description

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3175-3190
Author(s):  
Anvar Imomkulov ◽  
Victoria Velasco
Keyword(s):  
Three Dimensional ◽  
Time Dependent ◽  
Kolmogorov Equation ◽  
Natural Basis ◽  
3 Dimensional ◽  
Evolution Algebra ◽  
Fixed Rank ◽  
Weighted Digraph

In this paper we describe locally all the chains of three-dimensional evolution algebras (3-dimensional CEAs). These are families of evolution algebras with the property that their structure matrices with respect to a certain natural basis satisfy the Chapman-Kolmogorov equation. We do it by describing all 3-dimensional CEAs whose structure matrices have a fixed rank equal to 3, 2 and 1, respectively. We show that arbitrary CEAs are locally CEAs of fixed rank. Since every evolution algebra can be regarded as a weighted digraph, this allows us to understand and visualize time-dependent weighted digraphs with 3 nodes.

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