Collapses and Watersheds in Pseudomanifolds of Arbitrary Dimension

Cousty, Jean; Bertrand, Gilles; Couprie, Michel; Najman, Laurent

doi:10.1007/s10851-014-0498-z

Cited by 20 publications

(19 citation statements)

References 43 publications

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“…The interior can also be computed analogously. Note that somewhat similar operations are the (ultimate) collapses for cell complexes (Cousty et al, 2014).…”

Section: Closure Operationmentioning

confidence: 90%

“…One efficient and effective such encoding can be through a well chosen coordinate system. For other applications (see also x8 for details), such as boundary tracking (Herman, 1998;Klette & Rosenfeld, 2004), watershed transform (Cousty et al, 2014), thinning based on collapse (Kardos & Palá gyi, 2013) or morphological filters (Meyer & Angulo, 2007), the ability to access lower-dimensional cells is crucial. The pairing of these cells plays a critical role in Forman theory (Forman, 1998), which is the subject of increasing interest as a versatile topological analysis tool.…”

Section: Introductionmentioning

confidence: 99%

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A topological coordinate system for the diamond cubic grid

Čomić

Nagy

2016

Acta Cryst Sect A

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Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis.

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“…The interior can also be computed analogously. Note that somewhat similar operations are the (ultimate) collapses for cell complexes (Cousty et al, 2014).…”

Section: Closure Operationmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

A topological coordinate system for the diamond cubic grid

Čomić

Nagy

2016

Acta Cryst Sect A

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“…Since our method is effectively a translation of watershed cuts into hypergraphs, we refer the reader to the works by Cousty et al [8,7] for a performance comparison against other segmentation methods.…”

Section: Illustration Of the Methodsmentioning

confidence: 99%

Watersheds on Hypergraphs for Data Clustering

Dias

Mansour

Valdivia

et al. 2017

Lecture Notes in Computer Science

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Abstract. We present a novel extension of watershed cuts to hypergraphs, allowing the clustering of data represented as an hypergraph, in the context of data sciences. Contrarily to the methods in the literature, instances of data are not represented as nodes, but as edges of the hypergraph. The properties associated with each instance are used to define nodes and feature vectors associated to the edges. This rich representation is unexplored and leads to a data clustering algorithm that considers the induced topology and data similarity concomitantly. We illustrate the capabilities of our method considering a dataset of movies, demonstrating that knowledge from mathematical morphology can be used beyond image processing, for the visual analytics of network data. More results, the data, and the source code used in this work are available at https://github.com/015988/hypershed.

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“…tetraedra, triangles, edges, vertices) glued together according to certain rules. Recent studies investigated mathematical morphology in this framework, leading to morphological operators that can filter noise with respect to its dimension (Dias et al, 2011) and to links between the notions of watershed and of homotopy (Cousty et al, 2014). The framework of combinatorial maps, which provides another topology-endowed representation of discrete objects, has also been used to perform morphological filters of an image along watershed contours before building a hierarchy of segmentation (Brun et al, 2005).…”

Section: Beyond Graphs: Other Interesting Structuresmentioning

confidence: 99%

A graph-based mathematical morphology reader

Najman

Cousty

2014

Pattern Recognition Letters

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The two authors contributed equally to this work which received funding from the Agence Nationale de la Recherche, contract ANR-2010-BLAN-0205-03. ARTICLE INFO ABSTRACTArticle history:This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research.

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Collapses and Watersheds in Pseudomanifolds of Arbitrary Dimension

Cited by 20 publications

References 43 publications

A topological coordinate system for the diamond cubic grid

A topological coordinate system for the diamond cubic grid

Watersheds on Hypergraphs for Data Clustering

A graph-based mathematical morphology reader

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