In this paper, we present a robust image segmentation technique based on the Geodesic Convex Active Contour (GCAC) and the Chan-Vese (CV) model. The proposed algorithm overcomes the drawbacks of existing interactive image segmentation techniques which are heavily dependent upon the initial user input. Here, we propose to start with a Geodesic based contour before using the Chan-Vese model. Contrary to the basic Geodesic model and the Random Walk technique, our algorithm works with minimal input and is shown to be independent of the location of the input pixels provided by the user. The algorithm works by initiating a contour based on the Geodesic distance which is then used with the Chan-Vese model to further refine the segmentation results. The combination of region-based and boundary-based segmentation techniques ensures that the proposed algorithm works well with all types of images. We tested the proposed algorithm on several standard databases using both subjective and objective measures. Our experimental results show that the proposed algorithm outperforms existing approaches over indoor and outdoor images in terms of both processing time and segmentation accuracy.