This presentation introduces the integral connection between deep learning networks and operator-splitting methods, demonstrating how popular architectures such as UNet can be construed as operator-splitting schemes for control problems. Combining this connection and the Potts model, we introduce PottsMGNet and the Double-Well Net as novel approaches to two-phase image segmentation. PottsMGNet employs an optimal control formulation to effectively encapsulate the linear and nonlinear operations characteristic of neural networks. It demonstrates improved robustness against noise by incorporating networks and mathematical models. Double-Well Net provides a data-driven way to learn the region-force term in the Potts model. This work aims to enhance the understanding of the interplay between deep learning architectures and mathematical modeling paradigms in of image processing.