This paper describes a novel approach to automatically recover accurate correspondence over various shapes. In order to detect the features points with the capability in capturing the characteristics of an individual shape, we propose to calculate the skeletal representation for the shape curve through the medial axis transform. Employing this shape descriptor, mathematical landmarks are automatically identified based on the local feature size function, which embodies the geometric and topological information of the boundary. Before matching the resulting landmarks, shape correspondence is first approached by matching he major components of the shape curves using skeleton features. This helps in keeping the consecutive order and reducing the search space during the matching process. Point matching is then performed within each pair of corresponding components by solving a consecutive assignment problem. The effectiveness of this approach is demonstrated through experimental results on several different training sets of biomedical object shapes.