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Purpose  With the recent development of deep learning technologies, various neural networks have been proposed for fundus retinal vessel segmentation. Among them, the U-Net is regarded as one of the most successful architectures. In this work, we start with simplification of the U-Net, and explore the performance of few-parameter networks on this task.    Methods  We firstly modify the model with popular functional blocks and additional resolution levels, then we switch to exploring the limits for compression of the network architecture. Experiments are designed to simplify the network structure, decrease the number of trainable parameters, and reduce the amount of training data. Performance evaluation is carried out on four public databases, namely DRIVE, STARE, HRF and CHASE_DB1. In addition, the generalization ability of the few-parameter networks are compared against the state-of-the-art segmentation network.    Results  We demonstrate that the additive variants do not significantly improve the segmentation performance. The performance of the models are not severely harmed unless they are harshly degenerated: one level, or one filter in the input convolutional layer, or trained with one image. We also demonstrate that few-parameter networks have strong generalization ability.    Conclusion  It is counter-intuitive that the U-Net produces reasonably good segmentation predictions until reaching the mentioned limits. Our work has two main contributions. On the one hand, the importance of different elements of the U-Net is evaluated, and the minimal U-Net which is capable of the task is presented. On the other hand, our work demonstrates that retinal vessel segmentation can be tackled by surprisingly simple configurations of U-Net reaching almost state-of-the-art performance. We also show that the simple configurations have better generalization ability than state-of-the-art models with high model complexity. These observations seem to be in contradiction to the current trend of continued increase in model complexity and capacity for the task under consideration.    Supplementary Information  The online version contains supplementary material available at 10.1007/s11548-021-02340-1.

“Keep it simple, scholar”: an experimental analysis of few-parameter segmentation networks for retinal vessels in fundus imaging