scholarly journals Compatible adjacency relations for digital products

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2787-2803 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Automorphism Group ◽  
Digital Images ◽  
Cartesian Product ◽  
Digital Products ◽  
Local Isomorphism ◽  
Regular Covering ◽  
Study Product

The present paper studies compatible adjacency relations for digital products such as a C-compatible adjacency (or the LC-property in [21]), an S-compatible adjacency in [27] (or the LS-property in [21]),which are used to study product properties of digital images. Furthermore, to study an automorphism group of a Cartesian product of two digital coverings which do not satisfy a radius 2 local isomorphism, which remains open, the paper uses some properties of an ultra regular covering in [24]. By using this approach, we can substantially classify digital products.

scholarly journals Ultra regular covering space and its automorphism group

2010 ◽  
Vol 20 (4) ◽  
pp. 699-710 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Automorphism Group ◽  
Transformation Group ◽  
Covering Space ◽  
Fundamental Groups ◽  
Discrete Transformation ◽  
Local Isomorphism ◽  
Digital Space ◽  
Regular Covering ◽  
Digital Covering ◽  
Digital Spaces

Ultra regular covering space and its automorphism groupIn order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck's discrete transformation group) of a digital covering. By using these tools, we can calculate digital fundamental groups of some digital spaces and classify digital covering spaces satisfying a radius 2 local isomorphism (Boxer and Karaca, 2008; Han, 2006b; 2008b; 2008d; 2009b). However, for a digital covering which does not satisfy a radius 2 local isomorphism, the study of a digital fundamental group of a digital space and its automorphism group remains open. In order to examine this problem, the present paper establishes the notion of an ultra regular covering space, studies its various properties and calculates an automorphism group of the ultra regular covering space. In particular, the paper develops the notion of compatible adjacency of a digital wedge. By comparing an ultra regular covering space with a regular covering space, we can propose strong merits of the former.

scholarly journals Graphs With Stability Index One

1976 ◽  
Vol 22 (2) ◽  
pp. 212-220 ◽  
Author(s):  
D. A. Holton ◽  
J. A. Sims
Keyword(s):  
Automorphism Group ◽  
Large Class ◽  
Cartesian Product ◽  
Sufficient Conditions ◽  
Stability Index ◽  
Arbitrary Graph ◽  
Stability Properties ◽  
The Stability

AbstractWe consider the effect on the stability properties of a graph G, of the presence in the automorphism group of G of automorphisms (uv)h, where u and v are vertices of G, and h is a permutation of vertices of G excluding u and v. We find sufficient conditions for an arbitrary graph and a cartesian product to have stability index one, and conjecture in the latter case that they are necessary. Finally we exhibit explicitly a large class of graphs which have stability index one.

scholarly journals Digital products with $ PN_k $-adjacencies and the almost fixed point property in $ DTC_k^\blacktriangle $

2021 ◽  
Vol 6 (10) ◽  
pp. 11550-11567
Author(s):  
Jeong Min Kang ◽  
◽  
Sang-Eon Han ◽  
Sik Lee ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Digital Images ◽  
Fixed Point Property ◽  
The Other ◽  
Point Property ◽  
Digital Products ◽  
Adjacency Relation ◽  
Digital Product ◽  
New Concepts ◽  
Continuous Maps

<abstract><p>Given two digital images $ (X_i, k_i), i \in \{1, 2\} $, first of all we establish a new $ PN_k $-adjacency relation in a digital product $ X_1 \times X_2 $ to obtain a relation set $ (X_1 \times X_2, PN_k) $, where the term $ ''$$ PN $" means $ ''$pseudo-normal". Indeed, a $ PN $-$ k $-adjacency is softer or broader than a normal $ k $-adjacency. Next, the present paper initially develops both the notion of $ PN $-$ k $-continuity and a $ PN $-$ k $-isomorphism. Furthermore, it proves that these new concepts, the $ PN $-$ k $-continuity and a $ PN $-$ k $-isomorphism, need not be equal to the typical $ k $-continuity and a $ k $-isomorphism, respectively. Precisely, we prove that none of the typical $ k $-continuity (<italic>resp.</italic> typical $ k $-isomorphism) and the $ PN $-$ k $-continuity (<italic>resp.</italic> $ PN $-$ k $-isomorphism) implies the other. Then we prove that for each $ i \in \{1, 2\} $, the typical projection map $ P_i: X_1 \times X_2 \to X_i $ preserves a $ PN_k $-adjacency relation in $ X_1 \times X_2 $ to the $ k_i $-adjacency relation in $ (X_i, k_i) $. In particular, using a $ PN $-$ k $-isomorphism, we can classify digital products with $ PN_k $-adjacencies. Furthermore, in the category of digital products with $ PN_k $-adjacencies and $ PN $-$ k $-continuous maps between two digital products with $ PN_k $-adjacencies, denoted by $ DTC_k^\blacktriangle $, we finally study the (almost) fixed point property of $ (X_1 \times X_2, PN_k) $.</p></abstract>

scholarly journals Non-ultra regular digital covering spaces with nontrivial automorphism groups

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1205-1218 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Automorphism Group ◽  
Homotopy Theory ◽  
Automorphism Groups ◽  
Digital Images ◽  
Covering Space ◽  
Transformation Groups ◽  
Covering Spaces ◽  
Nontrivial Automorphism ◽  
Digital Covering

The study of digital covering transformation groups (or automorphism groups, discrete deck transformation groups) plays an important role in the classification of digital spaces (or digital images). In particular, the research into transitive or nontransitive actions of automorphism groups of digital covering spaces is one of the most important issues in digital covering and digital homotopy theory. The paper deals with the problem: Is there a digital covering space which is not ultra regular and has an automorphism group which is not trivial? To solve the problem, let us consider a digital wedge of two simple closed ki-curves with a compatible adjacency, i ?{1,2}, denoted by (X, k). Since the digital wedge (X, k) has both infinite or finite fold digital covering spaces, in the present paper some of these infinite fold digital covering spaces were found not to be ultra regular and further, their automorphism groups are not trivial, which answers the problem posed above. These findings can be substantially used in classifying digital covering spaces and digital images so that the paper improves on the research in Section 4 of [3] (compare Figure 2 of the present paper with Figure 2 of [3]), which corrects an error that appears in the Boxer and Karaca's paper [3] (see the points (0,0), (0,8), (6, -1) and (6,7) in Figure 2 of [3]).

scholarly journals Separability Number and Schurity Number of Coherent Configurations

10.37236/1509 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Sergei Evdokimov ◽  
Ilia Ponomarenko
Keyword(s):  
Automorphism Group ◽  
Regular Graph ◽  
Cartesian Product ◽  
Distance Regular Graph ◽  
Coherent Configuration ◽  
Hamming Graph ◽  
Point Set ◽  
Configuration Scheme ◽  
Positive Integers ◽  
Cyclotomic Scheme

To each coherent configuration (scheme) ${\cal C}$ and positive integer $m$ we associate a natural scheme $\widehat{\cal C}^{(m)}$ on the $m$-fold Cartesian product of the point set of ${\cal C}$ having the same automorphism group as ${\cal C}$. Using this construction we define and study two positive integers: the separability number $s({\cal C})$ and the Schurity number $t({\cal C})$ of ${\cal C}$. It turns out that $s({\cal C})\le m$ iff ${\cal C}$ is uniquely determined up to isomorphism by the intersection numbers of the scheme $\widehat{\cal C}^{(m)}$. Similarly, $t({\cal C})\le m$ iff the diagonal subscheme of $\widehat{\cal C}^{(m)}$ is an orbital one. In particular, if ${\cal C}$ is the scheme of a distance-regular graph $\Gamma$, then $s({\cal C})=1$ iff $\Gamma$ is uniquely determined by its parameters whereas $t({\cal C})=1$ iff $\Gamma$ is distance-transitive. We show that if ${\cal C}$ is a Johnson, Hamming or Grassmann scheme, then $s({\cal C})\le 2$ and $t({\cal C})=1$. Moreover, we find the exact values of $s({\cal C})$ and $t({\cal C})$ for the scheme ${\cal C}$ associated with any distance-regular graph having the same parameters as some Johnson or Hamming graph. In particular, $s({\cal C})=t({\cal C})=2$ if ${\cal C}$ is the scheme of a Doob graph. In addition, we prove that $s({\cal C})\le 2$ and $t({\cal C})\le 2$ for any imprimitive 3/2-homogeneous scheme. Finally, we show that $s({\cal C})\le 4$, whenever ${\cal C}$ is a cyclotomic scheme on a prime number of points.

Reduction in size of digital images: does it lead to less detectability or loss of diagnostic information?

1998 ◽  
Vol 27 (2) ◽  
pp. 93-96 ◽  
Author(s):  
C H Versteeg ◽  
G C H Sanderink ◽  
S R Lobach ◽  
P F van der Stelt
Keyword(s):  
Digital Images ◽  
Diagnostic Information

Development of a system for craniofacial analysis from monitor-displayed digital images

1999 ◽  
Vol 28 (2) ◽  
pp. 123-126 ◽  
Author(s):  
E Gotfredsen ◽  
J Kragskov ◽  
A Wenzel
Keyword(s):  
Digital Images

Authentication of Digital Image using Exif Metadata and Decoding Properties

2018 ◽  
pp. 335-341 ◽  
Author(s):  
D. P. Gangwar ◽  
Anju Pathania
Keyword(s):  
Digital Image ◽  
Digital Images ◽  
Software Tools ◽  
Robust Analysis

This work presents a robust analysis of digital images to detect the modifications/ morphing/ editing signs by using the image’s exif metadata, thumbnail, camera traces, image markers, Huffman codec and Markers, Compression signatures etc. properties. The details of the whole methodology and findings are described in the present work. The main advantage of the methodology is that the whole analysis has been done by using software/tools which are easily available in open sources.

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