The capability to compute a partition of a cluttered environment starting from the obstacles that lie in it enables the construction of a route connecting an initial point to a desired final one. In this paper, we revisit the convex lifting method for the computation of a suitable partition of the cluttered environment with the objective to propose a systematic procedure of reorganization of the cells within the partition in order to repel their boundaries from the obstacles. The ultimate goal is the construction of a connecting-path between an initial point and a final point characterized by a corridor with improved width guaranteeing the collision avoidance. The qualities of the corridors will impact the constraints on the motion of the controlled agent and consequently the real-time performance and robustness of the navigation in a cluttered environment.