Discrete Images, Objects, and Functions in Zn

Voss, Klaus

doi:10.1007/978-3-642-46779-0

Cited by 66 publications

(38 citation statements)

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“…One way is based on discrete (lattice) geometry, in particular integral geometry on the lattice and introduction of discrete Minkowski functionals; see Voss (1993). In the present paper the alternative view is taken, namely that the analysis of the discretised image aims at a good approximation of parameters or features of the original (i.e.…”

Section: Introductionmentioning

confidence: 99%

The Euler Number of Discretised Sets – Surprising Results in Three Dimensions

Ohser

Nagel²,

Schladitz³

2011

Image Anal Stereol

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The problem of estimating the Euler-Poincaré characteristic (Euler number for short) of a set in the 3d Euclidean space is considered, given that this set is observed in the points of a lattice. In this situation, which is typical in image analysis, the choice of an appropriate data-based discretisation of the set is crucial. Four versions of a discretisation method which is based on the notion of adjacency systems are presented; these versions are referred to as 14¡ 1¢ 14¡ 1£ , 14¡ 2¢ 14¡ 2£ , 6¢ 26£ , and 26¢ 6£ . A comparative assessment of the four approaches is performed with respect to the systematic error occuring in application to Boolean models. It is a surprising result that, except for 26¢ 6£ , the estimators yield infinitely large systematic errors when the lattice spacing goes to zero. Furthermore, the measurements of the Euler number from 3d data of autoclaved aerated concrete illustrate the influence of the choice of adjacency and the behaviour of the estimators.

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Section: Introductionmentioning

confidence: 99%

The Euler Number of Discretised Sets – Surprising Results in Three Dimensions

Ohser

Nagel²,

Schladitz³

2011

Image Anal Stereol

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“…Let P be a set of closed, bounded convex sets in R 3 ; the elements of P will be called tiles, 2 and the union of all the elements of P will be denoted by U(P). P will be called normal (or "locally finite") if, for any P ∈ P, the number of tiles that intersect P is finite.…”

Section: Strongly Normal Sets Of Tilesmentioning

confidence: 99%

“…Some authors [1] have studied digital geometry on other regular grids (in 2D: hexagonal or triangular), and other authors have generalized digital geometry to various types of abstract discrete spaces; for important examples of the general approach see [2,3].…”

Section: Introductionmentioning

confidence: 99%

The Digital Topology of Sets of Convex Voxels

Saha

Rosenfeld

2000

Graphical Models

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“…A graph G is a mathematical object defined by two inter-connected sets: a set V of points, and a subset E of V x V [6]. The (Fig.…”

Section: Neighbourhood Graphsmentioning

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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Discrete Images, Objects, and Functions in Zn

Cited by 66 publications

References 0 publications

The Euler Number of Discretised Sets – Surprising Results in Three Dimensions

The Euler Number of Discretised Sets – Surprising Results in Three Dimensions

The Digital Topology of Sets of Convex Voxels

Analysis of Cellular Microscopy Images by Means of Neighbourhood Graphs

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