scholarly journals On the Digital Cohomology Modules

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1451 ◽  
Author(s):  
Dae-Woong Lee
Keyword(s):  
Commutative Ring ◽  
Digital Image ◽  
Finite Subset ◽  
Digital Images ◽  
Continuous Functions ◽  
Contravariant Functor ◽  
Adjacency Relation ◽  
The Relationship ◽  
Cohomology Modules

In this paper, we consider the digital cohomology modules of a digital image consisting of a bounded and finite subset of Zn and an adjacency relation. We construct a contravariant functor from the category of digital images and digital continuous functions to the category of unitary R-modules and R-module homomorphisms via the category of cochain complexes of R-modules and cochain maps, where R is a commutative ring with identity 1R. We also examine the digital primitive cohomology classes based on digital images and find the relationship between R-module homomorphisms of digital cohomology modules induced by the digital convolutions and digital continuous functions.

scholarly journals Coalgebras on Digital Images

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2082
Author(s):  
Sunyoung Lee ◽  
Dae-Woong Lee
Keyword(s):  
Commutative Ring ◽  
Digital Images ◽  
Continuous Functions ◽  
Contravariant Functor ◽  
Fundamental Properties

In this article, we investigate the fundamental properties of coalgebras with coalgebra comultiplications, counits, and coalgebra homomorphisms of coalgebras over a commutative ring R with identity 1R based on digital images with adjacency relations. We also investigate a contravariant functor from the category of digital images and digital continuous functions to the category of coalgebras and coalgebra homomorphisms based on digital images via the category of unitary R-modules and R-module homomorphisms.

scholarly journals Digital fixed points, approximate fixed points, and universal functions

2016 ◽  
Vol 17 (2) ◽  
pp. 159 ◽  
Author(s):  
Laurence Boxer ◽  
Ozgur Ege ◽  
Ismet Karaca ◽  
Jonathan Lopez ◽  
Joel Louwsma
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Digital Images ◽  
Continuous Functions ◽  
Universal Functions ◽  
Approximate Fixed Point ◽  
Fixed Point Properties ◽  
Digitally Continuous ◽  
Approximate Fixed Point Property ◽  
The Relationship

A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).

Digital Ontologies: The Ideality of Form in/and Code Storage—or— Can Graphesis Challenge Mathesis?

Leonardo ◽  
2001 ◽  
Vol 34 (2) ◽  
pp. 141-145 ◽  
Author(s):  
Johanna Drucker
Keyword(s):  
Digital Media ◽  
Digital Image ◽  
Digital Images ◽  
Western Culture ◽  
Cultural Authority ◽  
Mathematical Basis ◽  
Digital File ◽  
History Of ◽  
Truth Claims ◽  
The Relationship

Digital media gain their cultural authority in part because of the perception that they function on mathematical principles. The relationship between digital images and their encoded files, and in other cases, between digital images and the algorithms that generate them as display, lends itself to a conviction that the image and the file are mutually interchangeable. This relationship posits a connection of identicality between the file and the image according to which the mathematical basis and the image seem to share similar claims to truth. Since the history of images within Western culture is fraught with charges of deception and illusion, the question arises whether the ontological condition of the digital image, its very existence and identity, challenges this tradition. Or, by contrast, does the material instantiation of images, in their display or output, challenge the truth claims of the mathematically based digital file?

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.

PERBANDINGAN METODE MD4 DAN SHA 384 UNTUK MENDETEKSI ORISINALITAS CITRA DIGITAL

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Lemcia Hutajulu ◽  
Hery Sunandar ◽  
Imam Saputra
Keyword(s):  
Digital Image ◽  
Detrimental Effect ◽  
Digital Images ◽  
Computer Crime ◽  
The Other ◽  
Image Manipulation ◽  
The Internet ◽  
Secret Key

Cryptography is used to protect the contents of information from anyone except those who have the authority or secret key to open information that has been encoded. Along with the development of technology and computers, the increase in computer crime has also increased, especially in image manipulation. There are many ways that people use to manipulate images that have a detrimental effect on others. The originality of a digital image is the authenticity of the image in terms of colors, shapes, objects and information without the slightest change from the other party. Nowadays many digital images circulating on the internet have been manipulated and even images have been used for material fraud in the competition, so we need a method that can detect the image is genuine or fake. In this study, the authors used the MD4 and SHA-384 methods to detect the originality of digital images, by using this method an image of doubtful authenticity can be found out that the image is authentic or fake.Keywords: Originality, Image, MD4 and SHA-384

scholarly journals Digital Graphic Documentation and Architectural Heritage: Deformations in a 16th-Century Ceiling of the Pinelo Palace in Seville (Spain)

2021 ◽  
Vol 10 (2) ◽  
pp. 85
Author(s):  
Juan Reinoso-Gordo ◽  
Antonio Gámiz-Gordo ◽  
Pedro Barrero-Ortega
Keyword(s):  
20Th Century ◽  
Digital Image ◽  
Digital Images ◽  
Laser Scanner ◽  
16Th Century ◽  
Southern Europe ◽  
Architectural Heritage ◽  
Digital Documentation ◽  
First Time

Suitable graphic documentation is essential to ascertain and conserve architectural heritage. For the first time, accurate digital images are provided of a 16th-century wooden ceiling, composed of geometric interlacing patterns, in the Pinelo Palace in Seville. Today, this ceiling suffers from significant deformation. Although there are many publications on the digital documentation of architectural heritage, no graphic studies on this type of deformed ceilings have been presented. This study starts by providing data on the palace history concerning the design of geometric interlacing patterns in carpentry according to the 1633 book by López de Arenas, and on the ceiling consolidation in the 20th century. Images were then obtained using two complementary procedures: from a 3D laser scanner, which offers metric data on deformations; and from photogrammetry, which facilitates the visualisation of details. In this way, this type of heritage is documented in an innovative graphic approach, which is essential for its conservation and/or restoration with scientific foundations and also to disseminate a reliable digital image of the most beautiful ceiling of this Renaissance palace in southern Europe.

scholarly journals Robust Gaussian Noise Detection and Removal in Color Images using Modified Fuzzy Set Filter

2020 ◽  
Vol 30 (1) ◽  
pp. 240-257
Author(s):  
Akula Suneetha ◽  
E. Srinivasa Reddy
Keyword(s):  
Image Quality ◽  
Mean Square Error ◽  
Fuzzy Set ◽  
Digital Image ◽  
Gaussian Noise ◽  
Digital Images ◽  
Structural Similarity ◽  
Fuzzy Rules ◽  
Mean Square ◽  
Image Edges

Abstract In the data collection phase, the digital images are captured using sensors that often contaminated by noise (undesired random signal). In digital image processing task, enhancing the image quality and reducing the noise is a central process. Image denoising effectively preserves the image edges to a higher extend in the flat regions. Several adaptive filters (median filter, Gaussian filter, fuzzy filter, etc.) have been utilized to improve the smoothness of digital image, but these filters failed to preserve the image edges while removing noise. In this paper, a modified fuzzy set filter has been proposed to eliminate noise for restoring the digital image. Usually in fuzzy set filter, sixteen fuzzy rules are generated to find the noisy pixels in the digital image. In modified fuzzy set filter, a set of twenty-four fuzzy rules are generated with additional four pixel locations for determining the noisy pixels in the digital image. The additional eight fuzzy rules ease the process of finding the image pixels,whether it required averaging or not. In this scenario, the input digital images were collected from the underwater photography fish dataset. The efficiency of the modified fuzzy set filter was evaluated by varying degrees of Gaussian noise (0.01, 0.03, and 0.1 levels of Gaussian noise). For performance evaluation, Structural Similarity (SSIM), Mean Structural Similarity (MSSIM), Mean Square Error (MSE), Normalized Mean Square Error (NMSE), Universal Image Quality Index (UIQI), Peak Signal to Noise Ratio (PSNR), and Visual Information Fidelity (VIF) were used. The experimental results showed that the modified fuzzy set filter improved PSNR value up to 2-3 dB, MSSIM up to 0.12-0.03, and NMSE value up to 0.38-0.1 compared to the traditional filtering techniques.

scholarly journals Visual form beyond traditional media——On the expression and construction of watercolor art in digital painting

2020 ◽  
Vol 189 ◽  
pp. 03013
Author(s):  
Shan Li
Keyword(s):  
Digital Media ◽  
Digital Image ◽  
Construction Process ◽  
Aesthetic Value ◽  
Traditional Media ◽  
Traditional Form ◽  
Digital Painting ◽  
New Space ◽  
The Aesthetic ◽  
The Relationship

In the context of the development of digital image era and digital media art, watercolor art, as a traditional form of painting, will inevitably experience a subversive change and transformation of painting methods and ideas. By analyzing the artistic expression and construction process of watercolor art in digital painting, this paper finds out the aesthetic value and significance of watercolor art in digital painting, discusses the relationship between traditional watercolor painting and digital painting and the new space of watercolor development in the future.

scholarly journals Implementasi Pengamanan Citra Digital Menggunakan Algoritma ICE

2020 ◽  
Vol 1 (3) ◽  
pp. 284
Author(s):  
Josua Alfiandi Sinuhaji
Keyword(s):  
Digital Image ◽  
Block Cipher ◽  
Digital Images ◽  
Source Code ◽  
Digital Imagery ◽  
The Subject ◽  
Data Theft ◽  
The Difference ◽  
Cryptographic Techniques ◽  
Rotation Function

Digital imagery is currently very widely used, so it is very vulnerable to data theft by unauthorized parties. In order to maintain the security of digital images can be done by using cryptographic techniques. Cryptographic techniques can encode digital images by encrypting them in the form of passwords that are not understood. ICE is a block cipher published by Kwan in 1997. This algorithm has a structure similar to DES, but with additional bit permutations that do not depend on the key in the rotation function. There are various types of ICE variants, namely Thin-ICE, ICE standard, and ICE-n. The difference between the three is the length of the keyword used and the number of rounds. The Thin-ICE algorithm uses 64 bits and 8 turns. The ICE standard uses 64 bits and 16 round keys. The ICE-n algorithm uses keys 64n bits and 16n turns. The use of this type of algorithm can be adjusted to the needs of users where Thin-ICE has the lowest level of security among the three, while ICE-n is the highest. This algorithm does not become the subject of a patent and the source code can be used freely.Keywords : Cryptography, Digital Image,Algorithm,ICE.

2-Visible Submodules and Fully 2-Visible Modules

2019 ◽  
pp. 1-6
Author(s):  
Mahmood S. Fiadh ◽  
Wafaa H. Hanoon
Keyword(s):  
Commutative Ring ◽  
Nonzero Ideal ◽  
The Relationship

Let be a -module, T is a commutative ring with identity and be a proper submodule of . In this paper we introduce the concepts of 2-visible submodules and fully 2-visible modules as a generalizations of visible submodules and fully visible modules resp., where is said to be 2-visible whenever for every nonzero ideal of and A -module is called fully 2-visible if for any proper submodule of it is 2-visible.Study some of the properties of these concepts also discuss the relationship 2-visible submodules and fully 2-visible modules with 2-pure submoules and other related submodules and modules resp. are given.

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