We introduce the use of geodesic distances and geodesic radius for calculating pairwise similarities needed in various graph cuts based methods. By using geodesics on an edge strength function we are able to calculate similarities between pixels in a more natural way. Our technique improves the speed and reliability of calculating similarities and leads to reasonably good image segmentation results. Our algorithm takes an edge strength function as its input and its speed is independent of the feature dimension or the distance measure used.