Active contour model is a typical and effective closed edge detection algorithm, which has been widely applied in remote sensing image processing. Since the variety of the image data source, the complexity of the application background and the limitations of edge detection, the robustness and universality of active contour model are greatly reduced in the practical application of edge extraction. This study presented a fast edge detection approach based on global optimization convex model and Split Bregman algorithm. Firstly, the proposed approach defined a generalized convex function variational model which incorporated the RSF model’s principle and Chan’s global optimization idea and could get the global optimal solution. Secondly, a fast numerical minimization scheme based on split Bregman iterative algorithm is employed for overcoming drawbacks of noise and others. Finally, the curve evolves to the target boundaries quickly and accurately. The approach was applied in real special sea ice SAR images and synthetic images with noise, fuzzy boundaries and intensity inhomogeneity, and the experiment results showed that the proposed approach had a better performance than the edge detection methods based on the GMAC model and RSF model. The validity and robustness of the proposed approach were also verified.