Monocular dot-density cues in random-dot stereograms

In the original random-dot stereograms (RDSs) invented by Julesz, binocular disparity could only take on values that were integral multiples of dot width. The other common method for constructing RDSs (the projection method) relaxes this restriction. However, the projection method can introduce dot-density cues into the monocular images. When polar projection is employed, density variation is introduced as an expression of perspective cues; when parallel projection is employed, there are no perspective cues, but density variation is nonetheless introduced whenever disparity varies as a function of horizontal position. de Vries, Kappers, and Koenderink [(1994) Vision Research, 34, 2409-2423] proposed to minimize the density cues by selecting half of the random dots from a uniform random distribution in the right-eye image, projecting them onto the cyclopean surface, and then projecting them back to the left eye image and vice versa. In this paper the precise nature of the density cues introduced by the projection method, and by de Vries et al.'s modification of that method, are derived. It is also shown that the projection method and its modification have very similar density cues near the medial sagittal plane when polar projection is employed, and that they have identical density cues over the entire random-dot field when parallel projection is employed.