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.