Polyhedral Representation and Adjacency Graph in n-dimensional Digital Images

Khachan, Mohammed; Chenin, Patrick; Deddi, Hafsa

doi:10.1006/cviu.2000.0859

Cited by 11 publications

(5 citation statements)

References 16 publications

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“…Each cell is either a vertex, an edge or a face parallel to the directions of the grid, or a cube corresponding to a tile of the grid. This reconstruction was called cubical complex by Khachan et al (2000) (Fig. 2).…”

Section: Euler-poincaré Measuresmentioning

confidence: 99%

Computation of Minkowski Measures on 2d and 3d Binary Images

Legland¹,

Kiêu²,

Devaux³

2011

Image Anal Stereol

175

121

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Minkowski functionals encompass standard geometric parameters such as volume, area, length and the Euler-Poincaré characteristic. Software tools for computing approximations of Minkowski functionals on binary 2D or 3D images are now available based on mathematical methods due to Serra, Lang and Ohser. Minkowski functionals can not be used to describe spatial heterogeneity of structures. This description can be performed by using Minkowski measures, which are local versions of Minkowski functionals. In this paper, we discuss how to extend the computation of Minkowski functionals to the computation of Minkowski measures. Approximations of Minkowski measures are computed using filtering and look-up table transformations. The final result is represented as a grey-level image. Approximation errors are investigated based on numerical examples. Convergence and non convergence of the measure approximations are discussed. The measure of surface area is used to describe spatial heterogeneity of a synthetic structure, and of an image of tomato pericarp.

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Section: Euler-poincaré Measuresmentioning

confidence: 99%

Computation of Minkowski Measures on 2d and 3d Binary Images

Legland¹,

Kiêu²,

Devaux³

2011

Image Anal Stereol

175

121

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“…But considering the adjacency pair (6, 26), h 0 = 3 and in this case the vertices v 1 to v 6 and edges e 1 , e 2 must be counting twice because they belong to separating two voxels, giving a genus=0. A binary volume dataset can be represented in a compact way by an OP (Khachan et al, 2000). Based on this fact, a previous approach (Ayala et al, 2012) computes χ and the genus of a binary volume dataset using expression 2.…”

Section: Background and Related Workmentioning

confidence: 99%

An Efficient Alternative to Compute the Genus of Binary Volume Models

Cruz-Matías

Ayala

2013

Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Inform

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In this paper we present a method to compute the Euler characteristic (χ) and the genus of a volume dataset. It uses an alternative decomposition model to represent binary volume datasets: the Compact Union of Disjoint Boxes (CUDB). The method is derived from the classical method used with a voxel model and the computation of χ and the genus is achieved by analyzing the connectivity among boxes and using a CUDB connectedcomponent labeling process. We have tested our method both with phantom and real datasets and we show that it is more efficient than previous methods based on the voxel model, and other alternative models.

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“…The following theorem expresses the fundamental properties that permit us to relate digital topology to Euclidean space topology. The proof of the above theorem and other properties related to the concept of continuous analogs in a binary (n + 1)-digital image are given in [10].…”

Section: Polyhedral Representation Of a Binary (N+1)-digital Imagementioning

confidence: 99%

Digital n-Pseudomanifold and n-Weakmanifold in a Binary (n + 1)-Digital Image

Khachan

Chenin

Deddi

2000

Discrete Geometry for Computer Imagery

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We introduce the notion of digital n-pseudomanifold and digital n-weakmanifold in (n+1)-digital image, in the context of (2n, 3 n −1)adjacency, and prove the digital version of the Jordan-Brouwer separation theorem for those classes. To accomplish this objective, we construct a polyhedral representation of the n-digital image, based on cubical complex decomposition. This enables us to translate some results from polyhedral topology into the digital space. Our main result extends the class of "thin" objects that are defined locally and verifies the Jordan-Brouwer separation theorem.

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Polyhedral Representation and Adjacency Graph in n-dimensional Digital Images

Cited by 11 publications

References 16 publications

Computation of Minkowski Measures on 2d and 3d Binary Images

Computation of Minkowski Measures on 2d and 3d Binary Images

An Efficient Alternative to Compute the Genus of Binary Volume Models

Digital n-Pseudomanifold and n-Weakmanifold in a Binary (n + 1)-Digital Image

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