The visualization of arteries and heart usually plays a crucial role in the clinical diagnosis, but researchers face the problems of region selection and mutual occlusion in clinical visualization. Therefore, the arteries and the heart cannot be easily visualized by current visualization methods. To solve the problems, we propose a new framework for arteries and cardiac visualization by combining a priori knowledge and the set operations. Firstly, a suitable region can be easily determined in the transfer function space with a priori knowledge and the visual feedback results. Secondly, the arteries and the heart can be directly extracted by the marked seed point. Finally, the arteries and the heart are separated for solving mutual occlusion through the set operations. This framework can easily solve the mutual occlusion problem in clinical visualization and greatly improve the region selection method in the transfer function space. Its effectiveness has been demonstrated on the basis of many experimental results.