User interaction with a display is detected using at least two cameras whose intersecting FOVs define a three-dimensional hover zone within which user interactions can be imaged. Each camera substantially simultaneously acquires from its vantage point two-dimensional images of the user within the hover zone. Separately and collectively the image data is analyzed to identify therein a relatively few landmarks definable on the user. A substantially unambiguous correspondence is established between the same landmark on each acquired image, and as to those landmarks a three-dimensional reconstruction is made in a common coordinate system. This landmark identification and position information can be converted into a command causing the display to respond appropriately to a gesture made by the user. 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.