Objective: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.