Characterizations of simple points, simple edges and simple cliques of digital spaces: One method of topology-preserving transformations of digital spaces by deleting simple points and edges

Evako, Alexander V.

doi:10.1016/j.gmod.2010.10.002

Cited by 5 publications

(6 citation statements)

References 22 publications

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“…Properties of contractible transformations were studied in [9] [14]. In particular, it was shown that contractible transformations do not change the Euler characteristic and the homology groups of graphs.…”

Section: An Induced Subgraph O(v) ⊆ G Containing All Vertices Of G Admentioning

confidence: 99%

“…Notice that in this paper, a subspace is an induced subspace. In papers [9] [13], digital n-surfaces and n-manifolds were defined and investigated. Definition 3.1 • A digital 0-dimensional surface (sphere) is a graph S 0 (x,y) with just two non-adjacent points x and y.…”

Section: An Induced Subgraph O(v) ⊆ G Containing All Vertices Of G Admentioning

confidence: 99%

“…A digital 2-surface M is called a digital 2-sphere if it is homotopy equivalent to a minimal digital 2-sphere [8] [9]. It can be checked directly that a digital 2-sphere G 6 depicted in Figure 5 can be converted to G 5 by a sequential contraction of simple pairs.…”

Section: Remark 31mentioning

confidence: 99%

“…G 7 and G 8 have no simple pairs, and cannot be converted to G 5 by sequential contractions of simple pairs. Properties of a digital sphere, a digital torus and a digital projective plane were studied in [8] [9]. Digital 2-surfaces can be used to construct topologically correct digital models of segmented medical images.…”

Section: Remark 31mentioning

confidence: 99%

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Topology Preserving Discretization Schemes for Digital Image Segmentation and Digital Models of the Plane

Evako¹

2014

OALib

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In this paper, discretization schemes are defined and studied that allow us to build digital models of 2-dimensional continuous objects with the same topological properties as their continuous counterparts. In particular, it is shown that the digital model of the plane is necessarily the digital 2-surface defined and studied in the context of digital topology. It is shown that in proposed discretization schemes, any required resolution can be used in any area of the object of interest. Finally, we describe a method, which transforms regions of interest produced by the image acquisition process into digital spaces with topological features of the regions.

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Section: An Induced Subgraph O(v) ⊆ G Containing All Vertices Of G Admentioning

confidence: 99%

Section: An Induced Subgraph O(v) ⊆ G Containing All Vertices Of G Admentioning

confidence: 99%

Section: Remark 31mentioning

confidence: 99%

Section: Remark 31mentioning

confidence: 99%

See 2 more Smart Citations

Topology Preserving Discretization Schemes for Digital Image Segmentation and Digital Models of the Plane

Evako¹

2014

OALib

Self Cite

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“…In the literature various methods for characterizing simple points have been proposed (Kong and Rosenfeld, 1989;Couprie and Bertrand, 2009;Evako, 2011). We adopt the approach based on counting the 26-and 6-components in the neighborhood of a point (Bertrand, 1994;Bertrand and Malandain, 1994).…”

Section: Simple Pointsmentioning

confidence: 99%

Statistical Analysis of the Local Strut Thickness of Open Cell Foams

Liebscher¹,

Redenbach²

2013

Image Anal Stereol

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Open cell foams are formed by an interconnected network of struts whose thickness varies locally. These variations are known to have an impact on the elastic and thermal properties of the foam. In this paper we quantify the local strut thickness by means of micro computed tomography (µCT) imaging. We develop a fully automatic algorithm to extract the foam's skeleton from a binary image and its topological decomposition into vertices and struts. This allows to estimate the thickness of individual strut segments by the Euclidean distance transform, where an appropriate correction for struts with nonspherical cross-sectional shape is applied. Conflating these estimates based on the strut lengths results in a strut thickness profile for the entire foam. Based on this profile we give a statistical justification that a strut thickness model should depend on the strut length. Furthermore, the investigation of polynomial models for the strut thickness profile by means of regression analysis leads to a new three-parameter strut thickness model.

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Towards Automated Quantitative Vasculature Understanding via Ultra High-Resolution Imagery

Wang

Sun

et al. 2014

Signal and Image Analysis for Biomedical and Life Sciences

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This chapter presents an approach to processing ultra high-resolution, large-size biomedical imaging data for the purposes of detecting and quantifying vasculature and microvasculature . Capturing early signs of any changes in vasculature may have significant values for early-diagnosis and treatment assessment due to the well understood observation that vascular changes precede cancerous growth and metastasis metastasis . With the advent of key enabling technologies for extremely high-resolution imaging, such as synchrotron radiation synchrotron radiation based computed tomography (CT) computed tomography , the required levels of detail have become accessible. However, these technologies also present challenges in data analysis. This chapter aims to offer some insights as to how these changes might be best dealt with. We argue that the necessary steps in quantitative understanding of vasculatures include targeted data enhancement enhancement , information reduction aimed at characterizing the linear structure of vessels vessels , and quantitatively describing the vessel hierarchy. We present results on cerebral and liver vasculatures of a mouse captured at the Shanghai Synchrotron Radiation Facility (SSRF). These results were achieved with a processing pipeline comprising of our empirically selected component for each of the above steps. Towards the end, we discuss how alternative and additional components may be incorporated for improved speed and robustness.

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Characterizations of simple points, simple edges and simple cliques of digital spaces: One method of topology-preserving transformations of digital spaces by deleting simple points and edges

Cited by 5 publications

References 22 publications

Topology Preserving Discretization Schemes for Digital Image Segmentation and Digital Models of the Plane

Topology Preserving Discretization Schemes for Digital Image Segmentation and Digital Models of the Plane

Statistical Analysis of the Local Strut Thickness of Open Cell Foams

Towards Automated Quantitative Vasculature Understanding via Ultra High-Resolution Imagery

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