A generally accepted notion in binocular vision is that we see the world as if viewed by a single eye, the cyclopean eye. A consequence of seeing the world from a single point in space is that the outlines of occluding and occluded surfaces have the same shape. We designed stereograms in which subjects aligned binocularly visible lines to each other. The lines were lying in different depth planes. In the vicinity of occluded areas, binocular alignment was achieved by alignment of the lines in the eye that viewed the monocularly visible details. Stereograms in which shapes of surfaces lying in different depth planes were compared to each other show that occluding and occluded surfaces do not have the same shape: a square surface occludes rectangular surfaces in other depth planes of which the horizontal widths are smaller than the vertical widths. This difference is perceived shape is not possible if the centre of binocular direction has a fixed position in the head.