Abstract: To address the issues of insufficient robustness and poor physical interpretability in deep learning methods for noisy image segmentation tasks, this study proposes an image segmentation network called variational model with mean curvature based tailored net (VMMC-TNet). The model innovatively integrates a physics-informed mean curvature phase-field model with the UNet architecture, combining the Cahn-Hilliard equation with a mean curvature term and the classical UNet structure to construct an end-to-end hybrid model. The study employs control variables and neural network approximation strategies, along with a tailored finite point method (TFPM) for numerical solution. Experimental results on test datasets with various types and intensities of noise, including Gaussian noise, salt-and-pepper noise, and Poisson noise, demonstrate that VMMC-TNet exhibits significant advantages in segmentation accuracy and edge preservation compared to existing methods, enhancing the model's robustness and stability under noise interference.