Admissible Perturbation of Demicontractive Operators within Ant Algorithms for Medical Images Edge Detection

Cristina Ticala,Ioana Zelina,Camelia-M Pintea

doi:10.3390/math8061040

Cristina Ticala, Ioana Zelina + Show 1 more

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https://doi.org/10.3390/math8061040

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Journal: Mathematics	Publication Date: Jun 26, 2020
Citations: 7	License type: CC BY 4.0

Affiliation: Technical University of Cluj-Napoca

Abstract

Nowadays, demicontractive operators in terms of admissible perturbation are used to solve difficult tasks. The current research uses several demicontractive operators in order to enhance the quality of the edge detection results when using ant-based algorithms. Two new operators are introduced, χ -operator and K H -operator, the latter one is a Krasnoselskij admissible perturbation of a demicontractive operator. In order to test the efficiency of the new operators, a comparison is made with a trigonometric operator. Ant Colony Optimization (ACO) is the solver chosen for the images edge detection problem. Demicontractive operators in terms of admissible perturbation are used during the construction phase of the matrix of ants artificial pheromone, namely the edge information of an image. The conclusions of statistical analysis on the results shows a positive influence of proposed operators for image edge detection of medical images.

Highlights

Admissible perturbation theory is a direction of research which unifies the main aspects of iterative approximating
The theory of admissible perturbations of an operator introduced by Rus in [1] opens a new direction of research and unifies major aspects of the iterative approximation of fixed point for single valued self operators
The current study introduces two new operators

Summary

Introduction

Admissible perturbation theory is a direction of research which unifies the main aspects of iterative approximating. The theory of admissible perturbations of an operator introduced by Rus in [1] opens a new direction of research and unifies major aspects of the iterative approximation of fixed point for single valued self operators. The admissible perturbation of a nonlinear operator was studied in detail in [2] and extended for the generalized pseudocontractive operators by Berinde, Khan and Fukhar-ud-din [3]. In [9] a weak convergence theorem in Hilbert spaces using admissible perturbations is introduced. A standard approach for admissible perturbations of demicontractive operators is provided in [10]

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