In this paper we introduce a new thinning algorithm, called MB, which is optimized with respect to the total number of elementary Boolean operators needed to perform it. We first emphasize the sound foundations of the algorithm, which is built by expressing into the Boolean language the three following constraints: (1) homotopy, (2) median axis and (3) isotropy. The MB algorithm benefits from both novel algorithmic ideas and systematic logic minimization. By hunting down any redundancy in the expressions of topological/geometrical features , we achieve a procedure that is: dramatically low-cost, as it is completely computed in 18 Boolean binary operators per iteration, and secondly, fully parallel, or one-single-pass, which guarantees that the number of iterations equals half the biggest object thickness.