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Exponential entropy-based multilevel thresholding using enhanced barnacle mating optimization

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Abstract

Multilevel Thresholding (MLT) is a prominent image segmentation research field that can effectively handle problems encountered while collecting meaningful information from a digital image. Most of the existing entropy-based Multilevel thresholding approaches use the logarithmic behaviour of Shannon’s entropy, which does not exist for all possible points with appropriate bounded value. To evade this problem, an entropy-based on exponential information gain function is introduced as the fitness function in this paper to improve the thresholding accuracy. This research also proposes an enhanced Barnacle Mating optimization algorithm (EBMO) for obtaining appropriate threshold values by maximising the fitness function. The enhancement over basic Barnacle mating optimization is achieved by incorporating an additional Gaussian mutation strategy and a random flow towards the best solution steps with the original algorithm. The involvement of these additional steps helps the algorithm to prevent it to be stagnated at a local minimum by boosting its exploration capability. To validate the proposed optimization algorithm, it has been tested with a set of well-known benchmark functions and the CEC 2014 test suite. The results obtained in various tests are then compared with other standard and state-of-art algorithms with the help of quantitative analysis such as average, median, and standard deviation of the fitness values over several runs, qualitative analysis, such as search history, trajectory, and average fitness history and statistical analysis using Friedman Rank test and found superior to all. A more detailed analysis of the obtained results was also conducted using post hoc Bonferroni–Dunn and Holm test to observe how the proposed EBMO algorithm is significantly different from others. A comparison of the proposed exponential entropy (EE) based multilevel thresholding using EBMO (EBMO-EE) with other optimization algorithms also presented. Various performance measures such as peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), feature similarity index (FSIM), and Uniformity Measures (UM) obtained from different standard benchmark images of varying dimension are considered. It has been observed that there is an improvement of the thresholding accuracy, using EBMO, about 2% to 4% over others.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Anil Neerukonda Institute of Technology & Sciences, Sangivalasa, Visakhapatnam, Andhra Pradesh, 531162, India

    Bibekananda Jena

  2. Faculty of Engineering and Technology, Siksha O Anusandhan, Bhubaneswar, Odisha, 751030, India

    Manoj Kumar Naik

  3. Department of Electronics and Telecommunication Engineering, Veer Surendra Sai University of Technology, Burla, Odisha, 768018, India

    Rutuparna Panda

  4. Faculty of Computing and Data Science, FLAME University, Lavale, Pune, Maharashtra, 412115, India

    Ajith Abraham

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Appendix

Appendix

Table 9

Table 9 Unimodal test function
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Table 10

Table 10 Scalable dimension multimodal test function
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Table 11

Table 11 Fixed dimension multimodal test function
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3-level thresholded images (k = 2) and their corresponding histograms

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6-level thresholded images (k = 5) and their corresponding histograms

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5-level thresholded images (k = 4) and their corresponding histograms

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9-level thresholded images (k = 8) and their corresponding histograms

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Thresholding result of the proposed (EBMO-EE) method on Group-1 test images with combined histogram

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Thresholding result of the proposed (EBMO-EE) method on Group-2 test images with combined histogram

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Jena, B., Naik, M.K., Panda, R. et al. Exponential entropy-based multilevel thresholding using enhanced barnacle mating optimization. Multimed Tools Appl 83, 449–502 (2024). https://doi.org/10.1007/s11042-023-15668-4

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