In this paper, we propose a multilevel segmentation methods of medical images based on the classical and quantum genetic algorithms. The Genetic Algorithm (GA) uses a binary coding while the Quantum Genetic Algorithm (QGA) uses the qubit encoding of individuals. The two evolutionary algorithms are employed to maximize efficiently Rényi, Masi and Shannon entropies for the purpose of multi-objects segmentation of medical images. The Particle Swarm Optimization algorithm (PSO) was also used for comparison reasons. The segmentation quality of the nine proposed approaches is assessed by means of the prevailing indices PSNR, SSIM and FSIM. The numerical results and the comparative study were carried out on a sample of twenty medical images. It was shown that the QGA outpaces the GA, and the PSO outperforms significantly the both algorithms in the optimization task. Finally, it was found that the Rényi entropy is more suitable for the purpose of medical image multilevel thresholding.

本文提出了一种基于经典和量子遗传算法的医学图像多层次分割方法。遗传算法（GA）使用二进制编码，而量子遗传算法（QGA）使用个人的量子位编码。为了医学图像的多目标分割，采用了两种进化算法来有效地最大化Rényi，Masi和Shannon熵。出于比较的原因，还使用了粒子群优化算法（PSO）。九种建议方法的分割质量通过现行指标PSNR，SSIM和FSIM进行评估。数值结果和比较研究是在二十张医学图像样本上进行的。结果表明，QGA超过了GA，在优化任务中，PSO的性能明显优于两种算法。最后，发现Rényi熵更适合用于医学图像多级阈值化。