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In the image-based visual servoing framework, image moments provide an appealing choice as visual features since they can be easily evaluated on any shape on the image plane, and do not require tracking and matching of individual geometric structures between distinct image frames (i.e., the so-called correspondence problem). However, computation of the moment interaction matrix still requires the knowledge of specific unmeasurable 3D quantities relative to the target object, quantities that are usually approximated in practical implementations. Therefore, in this paper we analyze the possibility to estimate on-line the value of such 3D quantities during the camera motion with the only assumption of a target shape with planar limb surface. The proposed estimation scheme builds upon the theory of nonlinear observers, and in particular exploits the basic formulation of the persistency of excitation Lemma. Simulation results are then presented in order to support the effectiveness of the proposed approach.