In this paper, we explore generalized direct-form II realization of two-dimensional separable-denominator digital filters of order (m,n) based on the concept of polynomial operators, where we deal with a model with 3(m + n) + mn + 1 fixed parameters plus m + n free parameters. An l₂-scaling method is introduced by utilizing different coupling coefficients at different branch nodes to avoid overflow. An expression for the roundoff noise gain in the realization is also examined. It is shown that the roundoff noise gain can be minimized with respect to the m + n free parameters by means of exhaustive search in a finite element space.