Component-Graph Construction

Passat, Nicolas; Naegel, Benoît; Kurtz, Camille

doi:10.1007/s10851-019-00872-5

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…This may open the way to efficient construction strategies compared e.g. to the componenthypertree [29], the component-graph [40] or the braid of partitions [58], the construction of which remains complex and/or costly.…”

Section: Links Between Usual and New Hierarchiesmentioning

confidence: 99%

Morphological Hierarchies: A Unifying Framework with New Trees

Passat,

Mendes Forte,

Kenmochi

2023

J Math Imaging Vis

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Morphological hierarchies constitute a rich and powerful family of graph-based structures that can be used for image modeling, processing and analysis. In this article, we focus on an important subfamily of morphological hierarchies, namely the trees that model partial partitions of the image support. This subfamily includes in particular the component-tree and the tree of shapes. In this context, we provide some new graph-based structures (one directed acyclic graph and three trees): the graph of valued shapes, the tree of valued shapes, the complete tree of shapes and the topological tree of shapes. These new objects create a continuum between the two notions of component-tree and tree of shapes. In particular, they allow to establish that these two trees (together with a third notion of adjacency tree generally considered in topological image analysis) can be defined and handled in a unified framework. In addition, this framework enables to enrich the component-tree with additional information, leading on the one hand to a topological description of grey-level images that relies on the same paradigm as persistent homology, and on the other hand to the proposal of a topological version of tree of shapes. This article provides a theoretical analysis of these new morphological hierarchies and their links with the usual ones. It also proposes an algorithmic description of two ways of building these new morphological hierarchies, and a discussion on the links that exist between these morphological hierarchies and certain topological invariants and descriptors.

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Section: Links Between Usual and New Hierarchiesmentioning

confidence: 99%

Morphological Hierarchies: A Unifying Framework with New Trees

Passat,

Mendes Forte,

Kenmochi

2023

J Math Imaging Vis

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“…This should open the way to efficient construction strategies, compared, e.g. to the component-hypertree [12], the component-graph [16] or the braid of partitions [29], the construction of which remains complex and/or costly.…”

Section: Links With Other Treesmentioning

confidence: 99%

A Topological Tree of Shapes

Passat

Kenmochi

2022

Lecture Notes in Computer Science

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In this article, we enrich the framework of morphological hierarchies with new acyclic graphs and trees. These structures lie at the convergence of hierarchical models and topological descriptors. We define them in the context of digital grey-level imaging. We discuss their links with component-trees, trees of shapes and adjacency trees. This analysis leads to new notions, including a notion of topological tree of shapes.

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“…An undirected graph G is set to correspond to this adjacency matrix. According to the adjacency matrix of the undirected graph G, the connected components [16,17] of undirected graph G were obtained after the calculation.…”

Section: Solving the Weighted Average Of The Mean Functional Concentration Ratios Of Enzyme Reactionsmentioning

confidence: 99%

The Relationship between Functional and Evolutionary Correlations of Enzyme Reactions in Metabolic Network Evolution

Hao

Shen

Xie

2021

Braz. arch. biol. technol.

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The evolution of species is inevitably accompanied by the evolution of metabolic networks to adapt to different environments. The metabolic networks of different species were collected from the Kyoto Encyclopedia of Genes and Genomes (KEGG) website, and some enzyme reactions with the highest occurrence frequency in all species were found and are reported in this paper. The correlation coefficients of whether the enzyme reactions appear in all species were calculated, and the corresponding evolutionary correlation connection networks were calculated according to different correlation coefficient thresholds. These studies show that, as the evolutionary correlation of enzyme reactions increases, the weighted average of the mean functional concentration ratios of the enzyme reactions also increases, indicating that the functional concentration ratio of enzyme reactions has a certain correlation with the evolutionary correlation. The work presented in this paper enhances our understanding of the characteristics and general rules of metabolic network evolution.

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Component-Graph Construction

Cited by 8 publications

References 21 publications

Morphological Hierarchies: A Unifying Framework with New Trees

Morphological Hierarchies: A Unifying Framework with New Trees

A Topological Tree of Shapes

The Relationship between Functional and Evolutionary Correlations of Enzyme Reactions in Metabolic Network Evolution

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