Graph cut based on color model is sensitive to statistical information of images. Integrating priority information into graph cut approach, such as the geodesic distance information, may overcome the well-known drawback of bias towards shorter paths that occurred frequently with graph cut methods. In this paper, a conditional random field (CRF) model is formulated to combine color model and geodesic distance information into a graph cut optimization framework. A discriminative model is used to capture more comprehensive statistical information for geodesic distance. A simple and efficient parameter learning scheme based on feature fusion is proposed for CRF model construction. The method is evaluated by applying it to segmentation of natural images, medical images and low contrast images. The experimental results show that the geodesic information obtained by learning can provide more reliable object features. The dynamic parameter learning scheme is able to select best cues from geodesic map and color model for image segmentation.