Enhancing Ant-Based Algorithms for Medical Image Edge Detection by Admissible Perturbations of Demicontractive Mappings

Vasile Berinde,Cristina Ţicală

doi:10.3390/sym13050885

Vasile Berinde, Cristina Ţicală

Open Access

https://doi.org/10.3390/sym13050885

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Abstract

The aim of this paper is to show analytically and empirically how ant-based algorithms for medical image edge detection can be enhanced by using an admissible perturbation of demicontractive operators. We thus complement the results reported in a recent paper by the second author and her collaborators, where they used admissible perturbations of demicontractive mappings as test functions. To illustrate this fact, we first consider some typical properties of demicontractive mappings and of their admissible perturbations and then present some appropriate numerical tests to illustrate the improvement brought by the admissible perturbations of demicontractive mappings when they are taken as test functions in ant-based algorithms for medical image edge detection. The edge detection process reported in our study considers both symmetric (Head CT and Brain CT) and asymmetric (Hand X-ray) medical images. The performance of the algorithm was tested visually with various images and empirically with evaluation of parameters.

Highlights

Iterative algorithms and, in particular, fixed point iterative algorithms, are important tools in the application of mathematical methods to problems arising in acoustic signal processing, optical imaging and medical tomography
The aim of this paper is to show analytically and empirically how ant-based algorithms for medical image edge detection can be enhanced by using an admissible perturbation of demicontractive operators
We complement the results reported in a recent paper by the second author and her collaborators, where they used admissible perturbations of demicontractive mappings as test functions

Summary

Introduction

In particular, fixed point iterative algorithms, are important tools in the application of mathematical methods to problems arising in acoustic signal processing, optical imaging and medical tomography. In a recent paper [2], to enhance the quality of the edge detection results in medical image processing when using ant-based algorithms, the authors used as test functions admissible perturbations of some demicontractive operators. The class of demicontractive mappings, which includes, among others, the class of nonexpansive mappings having a fixed point and the class of quasi-nonexpansive mappings, turned out to provide very convenient attenuation properties for medical images edge detection when using ant-based algorithms, as illustrated by the numerical tests reported by [2] and in Section 3 of the present paper. This work clearly shows that, in ant algorithms for medical images edge detection, the use of demicontractive operators and especially of the admissible perturbations of demicontractive operators is beneficial for the quality of the extracted edges. We give a brief account of the definition, connections and main properties of demicontractive mappings, as well as the notion and properties of the so-called admissible perturbation of an operator

Enriching Nonlinear Mappings by Admissible Perturbations

Admissible Perturbations of Demicontractive Mappings as Test Functions

Conclusions