This paper proposes a new approach for skeletonization based on the skeleton strength map (SSM) caculated by Euclidean distance transform of a binary image. After the distance transform and gradient are computed, isotropic diffusion is performed on the gradient vector field and the skeleton strength map is computed from the diffused vector field. A critical point set is then selected from local maxima of the SSM. The critical points are located on significant visual parts of the object. The skeleton is obtained by connecting the critical points with geodesic paths. This approach overcomes intrinsic drawbacks of distance transform based skeletons, since it yields stable and connected skeletons without losing significant visual parts.