Perceived Stereo Depth reflects Retinal Disparities, not 3D Geometry

We present a new illusion that challenges our traditional understanding of stereo vision. Traditional ‘Triangulation’ accounts of stereo vision back-project from points on the retina to points in the world. This requires that stereo vision incorporates how binocular disparities fall off with the viewing distance squared. By contrast, Linton proposes a ‘Minimal Model’ of stereo vision where perceived stereo depth is simply a function (most likely a linear function) of the amount of disparity on the retina. We present a new illusion (the ‘Linton Stereo Illusion’) to adjudicate between these two approaches. The illusion consists of a smaller circle (at 40cm) in front of a larger circle (at 50cm), with constant angular sizes throughout. We move the larger circle forward by 10cm (to 40cm) and then back again (to 50cm). The question is, what distance should we move the smaller circle forward and back to maintain a constant perceived separation between the circles? Constant physical distance (10cm) (‘Triangulation’) or constant disparity (6.7cm) (‘Minimal Model’)? Observers choose constant disparity. This leads us to four conclusions: First, perceived stereo depth appears to be best captured by the ‘Minimal Model’. There is no scaling of disparity with distance. Second, doubling disparity appears to double perceived depth, suggesting that perceived stereo depth is proportional to disparity. Third, changes in vergence appear to have no effect on perceived depth. Fourth, stereo ‘depth constancy’ appears to be a cognitive (not perceptual) phenomenon, reflecting our experience of a world distorted in perceived stereo depth.