3d shape and scene layout are often misperceived when viewing stereoscopic displays. For example, viewing from the wrong distance alters an object's perceived size and shape. It is crucial to understand the causes of such misperceptions so one can determine the best approaches for minimizing them. The standard model of misperception is geometric. The retinal images are calculated by projecting from the stereo images to the viewer's eyes. Rays are back-projected from corresponding retinal-image points into space and the ray intersections are determined. The intersections yield the coordinates of the predicted percept. We develop the mathematics of this model. In many cases its predictions are close to what viewers perceive. There are three important cases, however, in which the model fails: 1) when the viewer's head is rotated about a vertical axis relative to the stereo display (yaw rotation); 2) when the head is rotated about a forward axis (roll rotation); 3) when there is a mismatch between the camera convergence and the way in which the stereo images are displayed. In these cases, most rays from corresponding retinal-image points do not intersect, so the standard model cannot provide an estimate for the 3d percept. Nonetheless, viewers in these situations have coherent 3d percepts, so the visual system must use another method to estimate 3d structure. We show that the non-intersecting rays generate vertical disparities in the retinal images that do not arise otherwise. Findings in vision science show that such disparities are crucial signals in the visual system's interpretation of stereo images. We show that a model that incorporates vertical disparities predicts the percepts associated with improper viewing of stereoscopic displays. Improving the model of misperceptions will aid the design and presentation of 3d displays.

Keywords: 3D displays; Depth perception; Virtual Reality; Visualization.