An optical touch-sensitive device has the capability to determine touch locations of multiple simultaneous touch events. The touch events disturb optical beams propagating across the touch sensitive surface. With multi-touch events, a single beam can be disturbed by more than one touch event. In one aspect, a non-linear transform is applied to measurements of the optical beams in order to linearize the effects of multiple touch events on a single optical beam. In another aspect, the effect of known touch events (i.e., reference touches) is modeled in advance, and then unknown touch events are determined with respect to the reference touches.