Surface interpolation and illusory boundary formation in stereoscopic images: the role of local element properties

Abstract

Since White (1962) there have been many reports of the formation of illusory, depth-defined contours in sparse random-element stereograms. The most common example is that of the standard depth-defined square which floats above a random-element background. The boundaries of the square typically appear continuous and regular, in spite of the fact that there are large areas along the boundary containing no elements. Clearly in these instances the visual system employs an interpolation process to assign depth values to the ambiguous regions on either side of the boundary. The aim of these experiments was to identify constraints on this type of 3D interpolation/boundary formation, specifically, the role of local element attributes such as size and spacing on the perceived locations of depth-defined boundaries. Our stimulus was a sparse random dot stereogram depicting an 11.31° × 6.8° rectangular region in the plane of the screen with a 4.5° central square defined by 0.1° of horizontal disparity (2.5 cm) in depth. The monitor's display area was divided in half horizontally with the 3D test stimulus presented on the top portion. The same image was presented on the bottom half of the screen binocularly with zero disparity. The subject's task was to demarcate the boundary along the right edge of the disparate square in the 3D image using its 2D counterpart. To assess the effect of element properties on 3D surface interpolation we created versions of the test stimulus with gaps ranging from 0.6 to 3 deg., and separately varied element size and spacing. Results indicate that element spacing strongly influences interpolation and boundary formation but element size alone does not. We found that as average spacing increases subjects show increased interpolation across image gaps. These data show that 3D surface interpolation and the resultant boundary formation are not simply the result of local operations performed on isolated elements.