In the modern science and technology society, with the rapid development of digital image processing technology, image segmentation, and object edge detection are widely used in the medical, military, public defense, computer vision, and agricultural meteorology field. In this study, based on the classical Chan-Vese (CV) model, a piecewise constant image edge detection model with L1 norm data fitting term and TV2 second-order regular term is introduced. The new model uses a high-order regular function to penalize the objective function as a constraint on the new objective function, so that the model enabling to segment and detect images with low contrast and containing additional noise. Theoretically, we give reasonable assumptions, and a partial convergence analysis of the model is carried out. In terms of computation load, we study the theoretical solvability of the new model. Compulationally, for the numerical implementation of the model, the model is numerically solved by ADMM algorithm, and a new solution method is designed. A large number of numerical experiments were carried out with grayscale images and real images, and compared with the original CV model. The experimental results show that many advantages of the model with wide applications.