Based on the concept of polynomial operators, this paper explores generalized direct-form II structure and its state-space realization for two-dimensional separable-denominator digital filters of order (m, n) where a structure with 3(m+n)+mn+1 fixed parameters plus m+n free parameters is introduced and analyzed. An l₂-scaling method utilizing different coupling coefficients at different branch nodes to avoid overflow is presented. Expressions of evaluating the roundoff noise for the filter structure as well as its state-space realization are derived and investigated. The availability of the m+n free parameters is shown to be beneficial as the roundoff noise measures can be minimized with respect to these free parameters by means of an exhaustive search over a set with finite number of candidate elements. The important role these parameters can play in the endeavors of roundoff noise reduction is demonstrated by numerical experiments.