The active contour model (ACM) is one of the most successful methods for target detection in optical and medical images, but multiplicative speckle noise greatly interferes with its use in synthetic aperture radar (SAR) images. To overcome this difficulty, a convex ACM is proposed. First, a ratio distance is defined in terms of the probability density functions on both sides of the contour. This ratio is then introduced into the Chan and Vese (CV) model. Second, by combining the modified CV and region-scalable fitting models, the global intensity fitting and local intensity fitting forces both evolve the contour. Third, the energy of the combination model is then incorporated into Chan’s global minimization active contour framework so that the global minimum can be reached. Furthermore, the gradient term in the final energy function allows the proposed model to locate boundaries more quickly and accurately. Numerically, a dual formulation is utilized to solve the problem of active contour propagation toward target boundaries. Target detection experiments in real and simulated SAR images show that the proposed model outperforms classical region-based and hybrid ACMs in terms of efficiency and accuracy.