A multilevel biomedical image thresholding approach using the chaotic modified cuckoo search

Abstract

This article addresses this challenge and proposes a novel approach based on the modified cuckoo search and chaos theory. This article describes a novel approach for multilevel biomedical image segmentation based on the modified cuckoo search and chaos theory which is the major contribution to the literature. The modified cuckoo search approach helps to model the Lévy flight efficiently and the incorporation of the chaos theory helps to maintain the diversity in the population. The proposed approach helps to determine the optimal threshold values for a given number of thresholds. Four different objective functions are used to get the realistic segmented output which is essential in biomedical image analysis. Moreover, detailed analysis is also helpful in understanding the suitable objective function for biomedical image segmentation. This work also helps to choose suitable chaotic maps with different optimization algorithms. Hybridization of chaos theory and modified cuckoo search helps to overcome the local optima and to find the global optima cost-effectively. The chaos theory is incorporated in this proposed work to replace some solutions with some chaotic sequences to enhance the associated randomness with various phases which is beneficial to overcome the premature convergence and its related issues. The optimum setup is determined by investigating the effect of different chaotic maps along with some standard metaheuristic optimization approaches. Both qualitative and quantitative approaches are used to evaluate and compare the proposed approach. The proposed algorithm is compared with four state-of-the-art approaches. The obtained results clearly show that the proposed approach outperforms some state-of-the-art approaches in terms of both quantitative results and segmented output. On average, the proposed approach can achieve 255.8331 MSE, 24.07047 PSNR, 291.6077 mean, 0.038869 SD, 0.688655 SSIM, and 16.05358 s execution time (all for nine clusters). It can be observed that the proposed approach can determine the optimal set of clusters comparatively faster on most occasions, especially for the higher number of clusters.

Appendix I

See Tables 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37.

See Figs. 8, 9, 10, 11.

Table 22 Quantitative comparison of the number of iterations, MSE, and PSNR for four different numbers of thresholding levels using Otsu’s interclass variance as the objective function

Table 23 Quantitative comparison of the standard deviation and mean for four different numbers of thresholding levels using Otsu’s interclass variance as the objective function

Table 24 Quantitative comparison of the SSIM and the CPU execution time for four different numbers of thresholding levels using Otsu’s interclass variance as the objective function

Table 25 Quantitative comparison of $E_{{{\text{SEQA}}}}^{1d}$ and $E_{{{\text{SEQA}}}}^{2d}$ for four different numbers of thresholding levels using Otsu’s interclass variance as the objective function

Table 26 Quantitative comparison of the Number of iterations, MSE, and PSNR for four different numbers of thresholding levels using Kapur’s entropy as the objective function

Table 27 Quantitative comparison of the standard deviation and mean for four different numbers of thresholding levels using Kapur’s entropy as the objective function

Table 28 Quantitative comparison of the SSIM and the CPU execution time for four different numbers of thresholding levels using Kapur’s entropy as the objective function

Table 29 Quantitative comparison of the $E_{{{\text{SEQA}}}}^{1d}$ and $E_{{{\text{SEQA}}}}^{2d}$ for four different numbers of thresholding levels using Kapur’s entropy as the objective function

Table 30 Quantitative comparison of the Number of iterations, MSE, and PSNR for four different numbers of thresholding levels using Tsallis entropy as the objective function

Table 31 Quantitative comparison of the standard deviation and mean for four different numbers of thresholding levels using Tsallis entropy as the objective function

Table 32 Quantitative comparison of the SSIM and the CPU execution time for four different numbers of thresholding levels using Tsallis entropy as the objective function

Table 33 Quantitative comparison of the $E_{{{\text{SEQA}}}}^{1d}$ and $E_{{{\text{SEQA}}}}^{2d}$ for four different numbers of thresholding levels using Tsallis entropy as the objective function

Table 34 Quantitative comparison of the number of iterations, MSE, and PSNR for four different numbers of thresholding levels using Cross entropy as the objective function

Table 35 Quantitative comparison of the standard deviation and mean for four different numbers of thresholding levels using Cross entropy as the objective function

Table 36 Quantitative comparison of the SSIM and the CPU execution time for four different thresholding levels using cross entropy as the objective function

Table 37 Quantitative comparison of the $E_{{{\text{SEQA}}}}^{1d}$ and $E_{{{\text{SEQA}}}}^{2d}$ for four different numbers of thresholding levels using cross entropy as the objective function

Fig. 8

Segmented outcome by applying the proposed algorithm for different numbers of clusters using Kapur’s entropy

Fig. 9

Segmented outcome by applying the proposed algorithm for different numbers of clusters using Tsallis entropy

Fig. 10

Segmented outcome by applying the proposed algorithm for different numbers of clusters using Otsu’s Interclass variance

Fig. 11

Segmented outcome by applying the proposed algorithm for different numbers of clusters using cross entropy