Multi-center star shape is a prevalent object shape feature, which has proven effective in model-based image segmentation methods. However, the shape field function induced by the multi-center star shape is non-smooth, and directly applying it to the data-driven image segmentation network architecture design may lead to instability in backpropagation. This paper proposes a convex combination star (CCS) shape, possessing multi-center star shape properties, and has the advantage of effectively controlling the shape of the region through a smooth field function. The sufficient condition of the proposed CCS shape can be combined into the image segmentation neural network structure design through the bridge between the variational segmentation model and the activation function of the data-driven method. Taking Segment Anything Model (SAM) and its improved version as backbone networks, we have shown that the segmentation network architecture with CCS shape properties can greatly improve the accuracy of segmentation results.

For effective image segmentation, it is crucial to employ constraints informed by prior knowledge about the characteristics of the areas to be segmented to yield favorable segmentation outcomes. However, the existing methods have primarily focused on priors of specific properties or shapes, lacking consideration of the general global shape similarity from a Contour Flow perspective. Furthermore, naturally integrating this contour flow prior image segmentation model into the activation functions of deep convolutional networks through mathematical methods is currently unexplored. In this paper, we establish a concept of global shape similarity based on the premise that two shapes exhibit comparable contours. Furthermore, we mathematically derive a contour flow constraint that ensures the preservation of global shape similarity. We propose two implementations to integrate the constraint with deep neural networks. Firstly, the constraint is converted to a shape loss, which can be seamlessly incorporated into the training phase for any learning-based segmentation framework. Secondly, we add the constraint into a variational segmentation model and derive its iterative schemes for solution. The scheme is then unrolled to get the architecture of the proposed CFSSnet. Validation experiments on diverse datasets are conducted on classic benchmark deep network segmentation models. The results indicate a great improvement in segmentation accuracy and shape similarity for the proposed shape loss, showcasing the general adaptability of the proposed loss term regardless of specific network architectures. CFSSnet shows robustness in segmenting noise-contaminated images, and inherent capability to preserve global shape similarity.