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Cuckoo search with differential evolution mutation and Masi entropy for multi-level image segmentation

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Abstract

Since the beginning of the twenty-first century, the Cuckoo Search (CS) algorithm has emerged as one of the robust, flexible, fast, and easily implementable techniques for the global search to solve many complex problems over continuous spaces. CS operates like other Nature-Inspired Algorithms (NIOA) whose effectiveness significantly depends on the exploration and exploitation phases. CS already proofs its efficiency in solving real-world optimization problems in various application domains. In this study, the author tries to enhance the efficiency of the CS by incorporating six different mutation strategies of Differential Evolution (DE). The performance of the proposed CS variants has been investigated over Multi-level thresholding based image segmentation field as it is considered one of the dominant image segmentation techniques of the recent era. It is known that computation of the optimal set of thresholds is significantly influenced by the considered objective function, and it can be trapped into local optima. On the other hand, the computational time of Multi-level thresholding increases exponentially when the number of threshold points increases. To overcome these problems, this study introduces CS variants over this segmentation field, where Masi entropy is maximized to find the optimal threshold points. The experiment has been conducted on various color pathology images. The results of such a comparative study provide valuable insight and information to develop efficient CS variants using optimal or adaptive mutation strategies of DE.

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Abbreviations

d :

Number of dimensions

P a :

Probability of nest abandoned in the optimization technique

X i :

i-th solution within the optimization technique

N p :

Number of solutions in the population or population size

low :

Lower bound for a given dimension

up :

Upper bound for a given dimension

∂ :

Random variable belonging to [0,1]

Lévy():

Lévy distribution based random number

α :

Scaling Factor

Γ :

Gamma function

σ :

Standard deviation

β :

Parameter for Lévy distribution

v :

step length of Lévy distribution

x i, j :

j-th dimension of the i-th solution within the optimization technique

Ub j :

Upper bound of solution in j-th dimension

Lb j :

Lower bound of solution in j-th dimension

Uj :

Random variable drawn from uniform distribution for j-th dimension

f i :

Fitness of i-th solution

X gbest :

Global best solution

M :

Mutant vector

F1 & F2:

Scaling factors

r :

Random integer generated

i :

Solution within an optimization technique

gbest :

Global best

L :

Gray levels

th :

Threshold

h :

Normalized histogram

C 0, C 1 :

Classes in image

w o, w 1 :

Image class probabilities

E r(I| th):

Masi Entropy

Var(I i, j):

Local variance of image

I i, j :

local mean of image

μ VI :

The mean of local variance

σ VIVj :

covariance between the variances of two images

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Maulana Abul Kalam Azad University of Technology, Kolkata, West Bengal, India

    Swarnajit Ray

  2. Department of Computer Science and Application, Midnapore College (Autonomous), Paschim Medinipur, West Bengal, India

    Santanu Parai, Arunita Das & Krishna Gopal Dhal

  3. Department of Computer Science and Engineering, Government College of Engineering & Textile Technology, Serampore, West Bengal, India

    Prabir Kumar Naskar

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  1. Swarnajit Ray
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  2. Santanu Parai
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Correspondence to Krishna Gopal Dhal.

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Ray, S., Parai, S., Das, A. et al. Cuckoo search with differential evolution mutation and Masi entropy for multi-level image segmentation. Multimed Tools Appl 81, 4073–4117 (2022). https://doi.org/10.1007/s11042-021-11633-1

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