Interactive image segmentation is an important application in computer vision for selecting objects of interest in images. Several interactive segmentation methods are based on distance transform algorithms. However, the most known distance transform, geodesic distance, is sensitive to noise in the image and to seed placement. Recently, the Dahu pseudo-distance, a continuous version of the minimum barrier distance (MBD), is proved to be more powerful than the geodesic distance in noisy and blurred images. This paper presents a method for combining the Dahu pseudo-distance with edge information in a graph-cut optimization framework and leveraging each's complementary strengths. Our method works efficiently on both 2D/3D images and videos. Results show that our method achieves better performance than other distance-based and graph-cut methods, thereby reducing the user's efforts.