We propose a novel algorithm to jointly delineate the femoral artery lumen and outer wall surfaces from 3D black-blood MR images, while enforcing the spatial consistency of the reoriented MR slices along the medial axis of the femoral artery. We demonstrate that the resulting optimization problem of the proposed segmentation can be solved globally and exactly by means of convex relaxation, for which we introduce a novel coupled continuous max-flow (CCOMF) model based on an Ishikawa-type flow configuration and show its duality to the studied convex relaxed optimization problem. Using the proposed CCMF model, the exactness and globalness of its dual convex relaxation problem is proven. Experiment results demonstrate that the proposed method yielded high accuracy (i.e. Dice similarity coefficient > 85%) for both the lumen and outer wall and high reproducibility (intra-class correlation coefficient of 0.95) for generating vessel wall area. The proposed method outperformed the previous method, in terms of computation time, by a factor of pproximately 20.