This paper is devoted to presenting a new strategy for 3D objects recognition using a flexible similarity measure based on the recent modeling wave (MW) topology in spherical models. MW topology allows us to establish an n-connectivity relationship in 3D objects modeling meshes. Using the complete object model, a study on considering different partial information of the model has been carried out to recognize an object. For this, we have introduced a new feature called cone-curvature (CC), which originates from the MW concept. CC gives an extended geometrical surroundings knowledge for every node of the mesh model and allows us to define a robust and adaptable similarity measure between objects for a specific model database. The defined similarity metric has been successfully tested in our lab using range data of a wide variety of 3D shapes. Finally, we show the applicability of our method presenting experimentation for recognition on noise and occlusion conditions in complex scenes.