摘要目的:建立基于U-Net的四元数值神经网络(QU-Net)的眼底血管分割模型，并验证其对眼底影像视网膜血管提取和分割的精确度和效率。方法:采用超复数概念，使用彩色图片的3个通道，用四元矩阵表示彩色图片的所有信息数据；该四元矩阵用作四元卷积和四元数完全连接层的输入，基于U-Net架构进行计算，形成QU-Net模型。将QU-Net模型先在DRIVE、STARE和CHASE_DB1数据集上进行初始测试，与传统实数空间的U-Net、M-Net和SU-Net模型从准确率、敏感度、特异度、精确度、F1值和马修斯相关系数(MCC)等方面进行性能比较。进一步对该模型进行优化，并将优化后的QU-Net模型与国际上已知的先进模型进行横向比较，从而综合评估该模型在眼底影像血管分割提取方面的效率和准确性。结果:QU-Net模型在DRIVE数据集上血管分割的准确率为0.956 6，敏感度为0.700 8，特异度为0.987 9，精确度为0.595 4；在STARE数据集上，其准确率为0.975 5，敏感度为0.890 7，特异度为0.984 2，精确度为0.662 5；在CHASE_DB1数据集上，其准确率为0.979 4，敏感度为0.747 0，特异度为0.990 6，精确度为0.596 9。QU-Net模型的特异度优于U-Net、M-Net、SU-Net模型，其准确率、敏感度和精确度不弱于3个经典模型。对QU-Net模型进行优化后，在维持其原本准确率和特异度的基础上，优化模型在3个数据集上的敏感度、精确度和F1值均得到有效提高。将其与国际上其他已发表模型测试的各指标结果在3个数据集分别进行横向比较，发现优化的QU-Net模型的准确率、特异度、敏感度、精确度、F1值均表现良好，综合分析结果显示该模型的血管分割能力不弱于国际先进模型，在所有对比的模型中，优化的QU-Net模型的F1值和MCC表现最优。结论:本研究提出的QU-Net模型把数据维度空间从传统的实数空间提升至复数空间，大大减少了数据信息的损失；优化的QU-Net模型具有良好的眼底影像血管分割提取效率和准确性，并在检测细血管方面具有一定优越性。

abstractsObjective:To develop a U-Net-based quadruple numerical neural network (QU-Net) model for retinal vessel segmentation and to verify its precision and efficiency in extracting and segmenting retinal vessels from fundus images.Methods:This study used the concept of hypercomplex numbers, the three channels of color images, and a quaternion matrix representing all the information data of the images, which was then used as input for quaternion convolution and quaternion fully connected layers based on the U-Net architecture to form a QU-Net model.The QU-Net model was first tested on the DRIVE, STARE, and CHASE_DB1 datasets and compared with the traditional real-valued U-Net, M-Net, and SU-Net models in terms of accuracy, sensitivity, specificity, precision, F1 score, and Matthews correlation coefficient.Finally, the model was further optimized and the optimized QU-Net model was compared side-by-side with the well-known advanced models to comprehensively evaluate and analyze the efficiency and accuracy of the model in extracting and segmenting retinal blood vessels from fundus images.Results:The results showed that the QU-Net model achieved the following vessel segmentation results: accuracy 0.956 6, sensitivity 0.700 8, specificity 0.987 9, precision 0.595 4 on the DRIVE dataset, accuracy 0.975 5, sensitivity 0.890 7, specificity 0.984 2, precision 0.662 5 on the STARE dataset, and accuracy 0.979 4, sensitivity 0.747 0, specificity 0.990 6, precision 0.596 9 on the CHASE_DB1 dataset.Its specificity was better than U-Net, M-Net and SU-Net models, and its accuracy, sensitivity and precision were not inferior to the three models.After optimization, the sensitivity, precision and F1 value of the QU-Net model were effectively improved on the three datasets while maintaining its original accuracy and specificity.When compared with the performance indicators of other models on the three datasets, it was found that the optimized QU-Net model had good performance in accuracy, specificity, sensitivity, precision, and F1 score, indicating that its vessel segmentation ability was not inferior to the advanced models.Among all the models compared, the optimized QU-Net model had the best F1 score and Matthews correlation coefficient.Conclusions:The QU-Net model proposed in this study expands the data dimension space from the traditional real number space to the complex number space and greatly reduces the loss of data information.The optimized QU-Net model has good efficiency and accuracy in extracting retinal vessel segmentation from fundus images, and has certain advantages in detecting fine vessels.