A state-space model capable of representing 2-D transfer functions having separable denominators is introduced. The coordinates for the state space are chosen so that the number of adjustable scalar parameters in the model is minimized. This minimum-parameter model is used to approximate a 2-D filter by adjusting the model parameters so as to minimize a weighted sum of the squared difference between the 2-D filter and model impulse responses over the closed quarter-plane. This adjustment is done using the Davidon-Fletcher and Powell optimization algorithm. An example is given to illustrate the utility of the proposed method.