Abstract Multilevel thresholding (MLT) is one of the most widely used methods in image segmentation. However, the exhaustive search method is computationally time consuming for selecting the optimal thresholds. Consequently, heuristic algorithms are extensively used to reduce the complexity of the MLT problem. In this paper, an efficient Exchange Market Algorithm (EMA) is proposed to segment images using minimum cross entropy thresholding method. In the EMA, a market risk variable is used to balance the exploration and exploitation capabilities of the algorithm. Moreover, the local search capability is strengthened by the search and absorbent operators of EMA. Meanwhile, the most competent shareholders of EMA retain their best rank without undergoing any changes in their shares. These help in reducing the computational time. The proposed EMA based MLT is tested on benchmark and brain images with different threshold levels. Additionally, EMA approach is compared with other well-known algorithms such as, genetic algorithm, particle swarm optimization, bacterial foraging algorithm, firefly algorithm, honey bee mating optimization and teaching–learning based optimization. The experimental results show that the proposed EMA approach provides better outcomes than other algorithms.

中文翻译：

---

使用最小交叉熵辅助的多级阈值进行图像分割的交易策略

摘要 多级阈值（MLT）是图像分割中应用最广泛的方法之一。然而，穷举搜索方法在选择最佳阈值时计算耗时。因此，启发式算法被广泛用于降低 MLT 问题的复杂性。在本文中，提出了一种有效的交易所市场算法（EMA）来使用最小交叉熵阈值方法对图像进行分割。在 EMA 中，使用市场风险变量来平衡算法的探索和开发能力。此外，EMA 的搜索和吸收操作符增强了本地搜索能力。同时，EMA 最有能力的股东在其股份没有任何变化的情况下保持其最高级别。这些有助于减少计算时间。建议的基于 EMA 的 MLT 在具有不同阈值水平的基准和大脑图像上进行测试。此外，EMA 方法与其他著名算法进行了比较，例如遗传算法、粒子群优化、细菌觅食算法、萤火虫算法、蜜蜂交配优化和基于教学的优化。实验结果表明，所提出的 EMA 方法提供了比其他算法更好的结果。