A generalized filtering method based on the minimization of the energy of the Gibbs model is described. The well-known linear and median filters are all special cases of this method. It is shown that, with the selection of appropriate energy functions, the method can be successfully used to adapt the weights of the adaptive weighted median filter to preserve different textures within the image while eliminating the noise. The newly developed adaptive weighted median filter is based on a 3 x 3 square neighborhood structure. The weights of the pixels are adapted according to the clique energies within this neighborhood structure. The assigned energies to 2- or 3-pixel cliques are based on the local statistics within a larger estimation window. It is shown that the proposed filter performance is better compared to some well-known similar filters like the standard, separable, weighted and some adaptive weighted median filters.