In the context of motion detection, the endings (or terminators) of 1-D features can be detected as 2-D features, affecting the perceived direction of motion of the 1-D features (the barber-pole illusion) and the direction of tracking eye movements. In the realm of binocular disparity processing, an equivalent role for the disparity of terminators has not been established. Here we explore the stereo analogy of the barber-pole stimulus, applying disparity to a 1-D noise stimulus seen through an elongated, zero-disparity, aperture. We found that, in human subjects, these stimuli induce robust short-latency reflexive vergence eye movements, initially in the direction orthogonal to the 1-D features, but shortly thereafter in the direction predicted by the disparity of the terminators. In addition, these same stimuli induce vivid depth percepts, which can only be attributed to the disparity of line terminators. When the 1-D noise patterns are given opposite contrast in the two eyes (anticorrelation), both components of the vergence response reverse sign. Finally, terminators drive vergence even when the aperture is defined by a texture (as opposed to a contrast) boundary. These findings prove that terminators contribute to stereo matching, and constrain the type of neuronal mechanisms that might be responsible for the detection of terminator disparity.