Active contours and surfaces are deformable models used for 2D and 3D image segmentation. These models generally lack of convergence into boundary concavities, when segmenting highly concave objects. In this paper, we propose a method for exploring concavities, applicable on discrete active contours and surfaces deformed thanks to the greedy algorithm, which minimizes the energy functional. As a basis of this method, we introduce the gradient line energy (GLE), which goal is to make discrete parts of the surface coincide with boundaries, and the exploration force, computed from this energy, driving the surface into the object concavities. Our method lies on a general framework, enabling application on discrete 2D contours and 3D meshes with easy adaptation between both models.