Image segmentation is an essential digital image processing problem closely related to computer vision. The limitations of the total variational regular term for the continuous Potts model make the transition of segmentation results over-smooth. In this paper, we propose an improved model with prior conditions to realize the improvement of image segmentation results quality. To extract the structural features of the images, we utilize the simple and practical K-mean clustering (KM) algorithm to set the corresponding volume structure as a prior condition, which is also crucial for the initial label selection of the proposed model. Then, we choose two convex relaxation methods to solve the original nonconvex variational problem. Using these methods, we verify that increasing the constraint of volume structure can maintain slender structures in the original image and achieve a good balance between image segmentation quality and computation. Consequently, we use the unified, convergent primal-dual (PD) algorithm to solve the minimization problem in the proposed model. Extensive experimental comparisons between our method and the pure KM method, the graph-cut method, and the corresponding Potts model without volumetric structure are provided. The segmentation results illustrate that our model performs better in terms of both visualization and evaluation metrics.