In this paper, the problem of estimating the partial camera displacement from two images of a static object is studied. This scaled displacement is used to design a new vision-based control scheme, called 2D 1/2 visual servoing. It must be emphasized that motion and structure can be estimated without the a priori knowledge of a 3D model of the object, which increases the versatility and the application area of visual servoing. Since vision-based robotics tasks generally necessitate to be performed at video rate, we focus only on linear algorithms. The classical approach to linearly estimate the motion parameters is based on the computation of the essential matrix. In this paper, we propose another approach, based on the estimation of an homography matrix related to a chosen plane of an unknown object. Simulations and experiments on a real scene show that this method gives a more robust reconstruction of the motion parameters, especially in the singular cases. We then focus on the 2D 1/2 visual servoing scheme. This scheme is based on the estimation of the partial camera displacement from the current to the desired camera poses at each iteration of the control law. Visual features and data extracted from the partial displacement allow us to design a decoupled control law controlling the six camera d.o.f. The robustness of our visual servoing scheme with respect to camera calibration errors is also analyzed: the necessary and sufficient conditions for local asymptotic stability are easily obtained. Then, thanks to the simple structure of the system, sufficient conditions for global asymptotic stability are established. Finally, experimental results with an eye-in-hand robotic system confirm the improvement in the stability and robustness of the 2D 1/2 visual servoing with respect to classical position-based and image-based visual servoings.