This paper generalizes the previously developed automated edge-detection parameter selection algorithm of Yitzhaky and Peli. We generalize the approach to arbitrary multidimensional, continuous or discrete parameter spaces, and feature spaces. This generalization enables use of the parameter selection approach with more general image features, for use in feature-based multisensor image registration applications. We investigate the problem of selecting a suitable parameter space sampling density in the automated parameter selection algorithm. A real-valued sensitivity measure is developed which characterizes the effect of parameter space sampling on feature set variability. Closed-form solutions of the sensitivity measure for special feature set relationships are derived. We conduct an analysis of the convergence properties of the sensitivity measure as a function of increasing parameter space sampling density. For certain parameter space sampling sequence types, closed-form expressions for the sensitivity measure limit values are presented. We discuss an approach to parameter space sampling density selection which uses the sensitivity measure convergence behavior. We provide numerical results indicating the utility of the sensitivity measure for selecting suitable parameter values.