A methodological approach to the definition of nonlinear circuits for real-time image processing is presented. The image processing problem is formulated in terms of the minimization of a functional based on the Markov random fields (MRFs) theory. The terms of such a functional are related to the co-contents of proper nonlinear multiterminal resistors, thus reporting the minimization process to the achievement of an equilibrium solution in a circuit made up of these multiterminal resistors and of linear capacitors. Coupled image restoration and edge extraction in the presence of additive Gaussian noise are the specific problems addressed in this paper. Simulations show the ability of the proposed circuits to yield real-time solutions for these problems.