Segmentation is a crucial phase in image processing because it simplifies the representation of an image and facilitates its analysis. The multilevel thresholding method is more efficient for segmenting digital mammograms compared to the classic bi-level thresholding since it uses a higher number of intensities to represent different regions in the image. In the literature, there are different techniques for multilevel segmentation; however, most of these approaches do not obtain good segmented images. In addition, they are computationally expensive. Recently, statistical criteria such as Otsu, Kapur, and cross-entropy have been utilized in combination with evolutionary and swarm-based strategies to investigate the optimal threshold values for multilevel segmentation. In this paper, an efficient methodology for multilevel segmentation is proposed using the Harris Hawks Optimization (HHO) algorithm and the minimum cross-entropy as a fitness function. To substantiate the results and effectiveness of the HHO-based method, it has been tested over a benchmark set of reference images, with the Berkeley segmentation database, and with medical images of digital mammography. The proposed HHO-based solver is verified based on other comparable optimizers and two machine learning algorithms K-means and the Fuzzy IterAg. The comparisons were performed based on three groups. This first one is to provide evidence of the optimization capabilities of the HHO using the Wilcoxon test, and the second is to verify segmented image quality using the PSNR, SSIM, and FSIM metrics. Then, the third way is to verify the segmented image comparing it with the ground-truth through the metrics PRI, GCE, and VoI. The experimental results, which are validated by statistical analysis, show that the introduced method produces efficient and reliable results in terms of quality, consistency, and accuracy in comparison with the other methods. This HHO-based method presents an improvement over other segmentation approaches that are currently used in the literature.

分割是图像处理中的关键阶段，因为它简化了图像的表示并有助于对其进行分析。与经典的双级阈值相比，多级阈值方法对于分割数字乳房X线照片更有效，因为它使用更高数量的强度来表示图像中的不同区域。在文献中，有多种用于多层分割的技术。但是，这些方法大多数都无法获得良好的分割图像。另外，它们在计算上是昂贵的。近来，统计标准（例如Otsu，Kapur和交叉熵）已与进化和基于群体的策略结合使用，以研究用于多级细分的最佳阈值。在本文中，提出了一种有效的多级分割方法，该方法使用Harris Hawks优化（HHO）算法以及最小交叉熵作为适应度函数。为了证实基于HHO的方法的结果和有效性，已在基准基准图像集，伯克利分割数据库和数字化X线钼靶医学图像上进行了测试。基于其他可比较的优化器和两种机器学习算法对提出的基于HHO的求解器进行了验证K-均值和模糊IterAg。比较是基于三组进行的。第一个是使用Wilcoxon测试提供HHO优化功能的证据，第二个是使用PSNR，SSIM和FSIM指标验证分段图像的质量。然后，第三种方法是通过度量PRI，GCE和VoI验证分割图像与地面真实图像的比较。通过统计分析验证的实验结果表明，与其他方法相比，该方法在质量，一致性和准确性方面均能产生有效而可靠的结果。这种基于HHO的方法提出了对文献中当前使用的其他分割方法的改进。