This paper presents a novel variational and Partial Differential Equation (PDE)- based method to link edge points into closed contours. First, an ending point restrained energy function, which improves the one used in the Gradient Vector Flow (GVF) Snake model, is proposed to derive an ending point restrained Gradient Vector Flow (ERGVF) field. When there are broken edges in the edge map, the GVF field cannot recover the object¡¦s original shape, especially the broken corners of the object¡¦s boundary. The new ERGVF field can solve this problem by diffusing the gradient vectors in the continuous edge regions of the edge map into the broken edge regions. To detect the linked edge map based on the ERGVF field, this paper proposes a vector-based Mean Vector Difference (VMVD) method, which optimizes the original Mean Vector Difference (MVD) method by employing a new vector-based formula. The VMVD method has better performance than the MVD method when coping with images with broken edges. The proposed contour closure method can link broken edges belonging to multiple objects simultaneously and recover the objects¡¦ original shapes, especially the corners. Synthetic images with different edge structures and real cell images have been tested to show its validity and effectiveness in closed contour extraction and shape recovery.