Application of the Ring Theory in the Segmentation of Digital Images

Suárez, Yasel Garcés; Torres, Esley; Pereira, Osvaldo; Pérez, Claudia; Rodríguez, Roberto

doi:10.14810/ijscmc.2014.3405

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Cited by 5 publications

(2 citation statements)

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“…In 2013, the group theory was introduced for the spatial analysis in images [7] and later in [8]. The group theory was carried out considering the image like a matrix in which the elements belong to a cyclic group .…”

Section: The Mean Shift (mentioning

confidence: 99%

Edge Detection in Segmented Images Through Mean Shift Iterative Gradient ZnNusing Ring

Torres

Rodríguez

Suárez

et al. 2015

IJSCMC

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Section: The Mean Shift (mentioning

confidence: 99%

Edge Detection in Segmented Images Through Mean Shift Iterative Gradient ZnNusing Ring

Torres

Rodríguez

Suárez

et al. 2015

IJSCMC

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“…In mathematics, mainly in the area of algebra, ring theory has been studied in many researches and it has been applied in various fields such as computer science [1], cryptography [2] and image segmentation [3]. A set R is said to be a ring if it is an abelian group by addition, associative by multiplication and satisfies the left and right distributive law [4].…”

Section: Introductionmentioning

confidence: 99%

The Applications of Zero Divisors of Some Finite Rings of Matrices in Probability and Graph Theory

2020

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Let R be a finite ring. The zero divisors of R are defined as two nonzero elements of R, say x and y where xy = 0. Meanwhile, the probability that two random elements in a group commute is called the commutativity degree of the group. Some generalizations of this concept have been done on various groups, but not in rings. In this study, a variant of probability in rings which is the probability that two elements of a finite ring have product zero is determined for some ring of matrices over integers modulo n. The results are then applied into graph theory, specifically the zero divisor graph. This graph is defined as a graph where its vertices are zero divisors of R and two distinct vertices x and y are adjacent if and only if xy = 0. It is found that the zero divisor graph of R is a directed graph.

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