Efficient component-hypertree construction based on hierarchy of partitions

Morimitsu, Alexandre; Passat, Nicolas; Alves, Wonder Alexandre Luz; Hashimoto, Ronaldo Fumio

doi:10.1016/j.patrec.2020.02.032

Cited by 6 publications

(4 citation statements)

References 26 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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“…Algorithmic improvements for run-time execution and precision analysis are also proposed. Morimitsu et al (2020) propose an improved way of building the component-hypertree (that generalizes the concept of component-tree to multiple, increasing neighborhoods). They present some properties used to obtain optimized neighborhoods for component-hypertree computation.…”

Section: Contributionsmentioning

confidence: 99%