Parameter-tuning stochastic resonance has been successfully applied to one-dimensional signal processing. This paper explores the feasibility to extend this technique for image processing. Based on the two-dimensional nonlinear bistable dynamic system, the equation satisfied by the system output probability density function is derived for the first time. The corresponding equation for the one-dimensional system is the famous Fokker-Planck-Kolmogorov (FPK) equation. The stationary solution, eigenvalues and eigenfunctions of this equation are then investigated. The upper bound of the system response speed and the related calculation algorithm which are necessary for the applications of this technique to image processing are also proposed in this paper. Finally, the potential applications of this approach in image processing and some future research are suggested.