We assume that we have a pseudo-density-based design, e.g. obtained through classical SIMP topology optimization. Our objective is to find the optimal feature mapping parameterization to match the given design. Since feature mapping consists of higher-order geometric objects (e.g., bars and circles, see Wein, Dunning and Norato; 2020) mapped in a differentiable manner to a pseudo-density field with fixed discretization, we can formulate a tracking function to determine the optimal formulation. To solve this tracking problem effectively, we present a multistaged approach. In the initial stage, reaching the target density through the features is rewarded. The later tracking stage then also penalizes features not overlapping target design. We also introduce two techniques, which are also of relevance for general feature mapping optimization. Since feature mapping has essentially only a shape-sensitivity within the range of the boundary function (typically a symmetric cubic polynomial), we introduce an asymmetric boundary function with a long range outside the feature boundary to support moving features to distant target densities. Furthermore, we use second-order derivatives for appropriate boundary functions and achieve significant improvement in convergence against pseudo Hessians with IPOPT.