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This paper presents a visual-servoing method that is based on 2-D ultrasound (US) images. The main goal is to guide a robot actuating a 2-D US probe in order to reach a desired cross-section image of an object of interest. The method we propose allows the control of both in-plane and out-of-plane probe motions. Its feedback visual features are combinations of moments extracted from the observed image. The exact analytical form of the interaction matrix that relates the image-moments time variation to the probe velocity is developed, and six independent visual features are proposed to control the six degrees of freedom of the robot. In order to endow the system with the capability of automatically interacting with objects of unknown shape, a model-free visual servoing is developed. For that, we propose an efficient online estimation method to identify the parameters involved in the interaction matrix. Results obtained in both simulations and experiments validate the methods presented in this paper and show their robustness to different errors and perturbations, especially those inherent to the noisy US images.