Abstract: A new method of extracting the curve-skeleton of the objects is proposed. The gradient of the distance transform, which obtains a vector field and is valuable for extracting curve-skeleton, is used to detect critical points inside the objects. Each critical point represents a convex segment of the object. Then, the critical points are connected through searching the shortest gradient path, and thus, the curve-skeleton of the object is obtained. The method proposed in this paper is insensitive to the boundary noise, and the topological and geometrical features of the object can be represented by the extracted curve-skeleton. Furthermore, compared with other methods based on distance transform, the proposed method guarantees the connectivity of the curve-skeleton. The extracted curve-skeleton can be applied to objects recognition, matching and so on. The results of experiments on a large number of 2D and 3D objects are satisfying.