&lt;title&gt;Neighborhood graphs and image processing&lt;/title&gt;

Angot, François; Clouard, Régis; Elmoataz, Abderrahim; Revenu, Marinette

doi:10.1117/12.248541

Cited by 2 publications

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“…That is, for a given set of points and the connections between them, the RNG is the subset of those connections such that, for points

i

and j and their edge,

d_{i j}

, there are no connections

d_{k j}

d_{k i}

that are both shorter than

d_{i j}

. The RNG has been used extensively for feature recognition in the field of computational image analysis, among other applications (Rocha & Pavlidis, ; Angot et al ., ; Watanabe, ). For a set of points and connections between them, the MST is defined as the collection of connections such that every point is connected to every other point with the minimum total connection distance or weight (Graham & Hell, ).…”

Section: Introductionmentioning

confidence: 97%

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

Carson

Levine

2016

Journal of Microscopy

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The concept of a finite body Dirichlet tessellation has been extended to that of a finite body Delaunay 'triangulation' to provide a more meaningful description of the spatial distribution of nonspherical secondary phase bodies in 2- and 3-dimensional images. A finite body triangulation (FBT) consists of a network of minimum edge-to-edge distances between adjacent objects in a microstructure. From this is also obtained the characteristic object chords formed by the intersection of the object boundary with the finite body tessellation. These two sets of distances form the basis of a parsimonious homogeneity estimation. The characteristics of the spatial distribution are then evaluated with respect to the distances between objects and the distances within them. Quantitative analysis shows that more physically representative distributions can be obtained by selecting subgraphs, such as the relative neighbourhood graph and the minimum spanning tree, from the finite body tessellation. To demonstrate their potential, we apply these methods to 3-dimensional X-ray computed tomographic images of foamed cement and their 2-dimensional cross sections. The Python computer code used to estimate the FBT is made available. Other applications for the algorithm - such as porous media transport and crack-tip propagation - are also discussed.

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“…That is, for a given set of points and the connections between them, the RNG is the subset of those connections such that, for points

i

and j and their edge,

d_{i j}

, there are no connections

d_{k j}

d_{k i}

that are both shorter than

d_{i j}

Section: Introductionmentioning

confidence: 97%

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

Carson

Levine

2016

Journal of Microscopy

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“…hierarchical segmentation problems solved by bottom-up strategies [1], when starting with an over-segmented image and building a graph representing each region with both intrinsic and relational attributes [2]; region-merging and region-growing methods can be replaced by graph contractions and calculations of new attributes, e problems dealing with a population of objects and their neighbourhood relations [3], as in several histological applications; in cellular sociology [4], relations between the functional state of the cells and their spatial distribution within the tissue are studied; in the quantitative analysis of the tissue architecture, the distribution of one kind of cells within another is quantified [5].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Cellular Microscopy Images by Means of Neighbourhood Graphs

Angot

Elmoataz

Revenu

et al. 1996

Microsc. Microanal. Microstruct.

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Résumé. 2014 Abstract. 2014 Many image processing and image analysis problems, in two or three dimensions, can be addressed and solved by methods and tools developed within the graph theory. In this paper, an image representation based on graphs is proposed: a data structure, together with methods for attributing and weighting the graph, methods to merge nodes, etc. In order to demonstrate the interest of the approach, two applications dealing with 2D-images of cellular microscopy are described and discussed.

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<title>Neighborhood graphs and image processing</title>

Cited by 2 publications

References 0 publications

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application

Analysis of Cellular Microscopy Images by Means of Neighbourhood Graphs

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