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Image segmentation is an essential step in medical image analysis, as its results directly affect the quality of the follow-up analysis. Because of the high calculation speed and the good performance of the segmentation algorithms based on neural networks (NNs), image segmentation has been extensively researched and developed in clinical analysis and applications. However, the existing NN-based image segmentation methods only consider the pixel information of the image that needs to be segmented, and they cannot guarantee the continuity and smoothness of the segmented edge. Consequently, we propose the model and data-driven hybrid approach, namely, the model-data-driven hybrid-fusion network for medical image segmentation. We consider the attention mechanism and the high-low features, and embed the traditional curvature regularisation segmentation model into the NN in the form of a loss function. Moreover, our model considers not only the semantic information of the segmented image but also the boundary length information of the ROI and the target region information. These can ensure the smoothness of the edge of the medical image segmentation results. We conduct intensive experiments on several benchmark datasets to evaluate the effectiveness of our method in dealing with complex backgrounds and noise. Experimental results demonstrate that the proposed model outperforms other state-of-the-art segmentation methods. • We propose a loss function that combines contour length and region information and adds an elastic energy term to it, which tackles the problem of the unsmooth borders caused by purely network training. • We introduce a curvature based regularization function into the segmentation model to regularize the contour length term and improve the over-fitting phenomenon in network training. • We use a new network of a dual-path feature extraction module (DP-FEM) with channel attention and a high-level and low-level feature fusion module (HLFFM) with spatial attention, which improves the accuracy of training. • The results of the proposed fusion network segmentation are analysed with multiple existing models. The results prove that our proposed model can obtain reasonable image segmentation results on datasets, such as remote projection and fundus colour images. [ABSTRACT FROM AUTHOR]