A position detection system includes at least two optical units configured to image a space, a memory, and a processing device interfaced to the memory and the optical units. The processing device is configured to access image data from the first and second optical units and use this data to determine at least one of a current first position and a current second position representing touch points on a display. The processing device can define a polygon having at least four sides based the current first and current second positions and can access the memory to store and retrieve the polygon. If the processing device can determine only one of the current first position or the current second position based on the accessed image data, the processing device can use the previously defined polygon to estimate the other position that was not determined using the accessed image data.