User interaction with a display is detected substantially simultaneously using at least two cameras whose intersecting FOVs define a three-dimensional hover zone within which user interactions can be imaged. Separately and collectively image data is analyzed to identify a relatively few user landmarks. A substantially unambiguous correspondence is established between the same landmark on each acquired image, and a three-dimensional reconstruction is made in a common coordinate system. Preferably cameras are modeled to have characteristics of pinhole cameras, enabling rectified epipolar geometric analysis to facilitate more rapid disambiguation among potential landmark points. Consequently processing overhead is substantially reduced, as are latency times. Landmark identification and position information is convertible into a command causing the display to respond appropriately to a user gesture. Advantageously size of the hover zone can far exceed size of the display, making the invention usable with smart phones as well as large size entertainment TVs.