System for monitoring 3D space in front of an output unit for the control of the output unit, comprising: a 3D imaging unit, a processing and control unit coupled to the 3D imaging unit, and an output unit comprising a display area and coupled to the processing and control unit, wherein the 3D imaging unit is configured to monitor an interaction zone in front of the display area of the output unit, the processing and control unit is configured to predict where a finger of a hand that approaches the display area of the output unit and is monitored by the 3D imaging unit will touch the display area and to control the output unit to modify content displayed on the display area based on the predicted touch position, the system being characterized in that, the processing and control unit is configured to localize a finger tip and a finger base of the finger and to fit a line (52, 53) through the finger tip and the finger base, the processing and control unit is configured to compute an intersection point of the line (52, 53) through the finger tip and the finger base with the display area (14, 54), the processing and control unit comprises a 2D map representing the display area (14, 54) and comprising a plurality of cells, and the processing and control unit is configured to compute the intersection point of the line (52, 53) with the display area (14, 54) in consecutive time steps, wherein for each of the time steps at least one of the cells is identified corresponding to the computed intersection point and a numeric value assigned to the at least one identified cell is incremented, and the processing and control unit is configured to find peaks in the 2D map for each of the time steps in order to identify the predicted touch position of the finger. a 3D imaging unit, a processing and control unit coupled to the 3D imaging unit, and an output unit comprising a display area and coupled to the processing and control unit, wherein the 3D imaging unit is configured to monitor an interaction zone in front of the display area of the output unit, the processing and control unit is configured to predict where a finger of a hand that approaches the display area of the output unit and is monitored by the 3D imaging unit will touch the display area and to control the output unit to modify content displayed on the display area based on the predicted touch position, the system being characterized in that, the processing and control unit is configured to localize a finger tip and a finger base of the finger and to fit a line (52, 53) through the finger tip and the finger base, the processing and control unit is configured to compute an intersection point of the line (52, 53) through the finger tip and the finger base with the display area (14, 54), the processing and control unit comprises a 2D map representing the display area (14, 54) and comprising a plurality of cells, and the processing and control unit is configured to compute the intersection point of the line (52, 53) with the display area (14, 54) in consecutive time steps, wherein for each of the time steps at least one of the cells is identified corresponding to the computed intersection point and a numeric value assigned to the at least one identified cell is incremented, and the processing and control unit is configured to find peaks in the 2D map for each of the time steps in order to identify the predicted touch position of the finger.