Novel edge-enhancing filters called the selective average (SA) and the selective median (SM) filters are proposed. It is shown theoretically and experimentally that these filters enhance blurred edges while attenuating noise. Root structures of the SA and SM filters are studied. An efficient implementation of the SA filter that requires only one multiplier, four additions, and one comparison irrespective of the filter length is introduced. Comparisons of the SA and SM filters with other edge-enhancing techniques indicate that the proposed filters are simpler to implement, and that they perform better than the others.