Multilevel image thresholding is an essential step in the image segmentation process. Expectation Maximization (EM) is a powerful technique to find thresholds but is sensitive to the initial points. Differential Evolution (DE) is a robust metaheuristic algorithm that can find thresholds rapidly. However, it may be trapped in the local optimums and premature convergence occurs. In this paper, we incorporate EM algorithm to DE and introduce a novel algorithm called EM+DE which overcomes these shortages and can segment images better than EM and DE algorithms. In the proposed method, EM estimates Gaussian Mixture Model (GMM) coefficients of the histogram and DE tries to provide good volunteer solutions to EM algorithm when EM converges in local areas. Finally, DE fits GMM parameters based on Root Mean Square Error (RMSE) to reach the fittest curve. Ten standard test images and six famous metaheuristic algorithms are considered and result on global fitness. PSNR, SSIM, FSIM criteria and the computational time are given. The experimental results prove that the proposed algorithm outperforms the EM and DE as well as EM+ other natural-inspired algorithms in terms of segmentation criteria.

多级图像阈值处理是图像分割过程中必不可少的步骤。期望最大化 (EM) 是一种寻找阈值的强大技术，但对初始点很敏感。差分进化 (DE) 是一种强大的元启发式算法，可以快速找到阈值。然而，它可能被困在局部最优解中并发生早熟收敛。在本文中，我们将 EM 算法与 DE 相结合，并引入了一种称为 EM+DE 的新算法，该算法克服了这些不足，并且可以比 EM 和 DE 算法更好地分割图像。在所提出的方法中，EM 估计直方图的高斯混合模型 (GMM) 系数，当 EM 在局部区域收敛时，DE 尝试为 EM 算法提供良好的自愿解决方案。最后，DE 基于均方根误差 (RMSE) 拟合 GMM 参数以达到最适合的曲线。考虑了十个标准测试图像和六个著名的元启发式算法，并得出全局适应度的结果。给出了 PSNR、SSIM、FSIM 标准和计算时间。实验结果证明，所提出的算法在分割标准方面优于EM和DE以及EM+其他自然启发算法。