Perception, 1996, volume 25, pages 165-176 Pooling of vertical disparities by the human visual system Wendy Adams, John P Frisby, David Buckley, Jonas Garding#, Stephen D Hippisley-Cox, John Porrill Al Vision Research Unit, University of Sheffield, Sheffield S10 2TN, UK; # Department of Numerical Analysis and Computer Science, Royal Institute of Technology, Stockholm, Sweden Received 12 July 1995, in revised form 1 December 1995 Abstract. Two experiments are described in which the effects of scaling vertical disparities on the perceived amplitudes of dome-shaped surfaces depicted with horizontal disparities were examined. The Mayhew and Longuet-Higgins's theory and the regional-disparity-correction theory of Gafding et al predict that scaling should generate a change in perceived depth appropriate to the viewing distance simulated by the scaled vertical disparities. Significant depth changes were observed, by means of a nulling task in which the vertical-disparity-scaling effect was cancelled by the observer choosing a pattern of horizontal disparities that made the dome-shaped surface appear flat. The sizes of the scaling effects were less than those predicted by either theory, suggesting that other cues to fixation distance such as oculomotor information played an appre- ciable role. In conditions in which 50% of the texture elements were given one value of vertical- disparity scaling and the remaining 50% were left unsealed, the size of the scaling effect on perceived depth could be accounted for by equally weighted pooling of the vertical-disparity information unless the two scalings were very dissimilar, in which case the lower scaling factor tended to dominate. These findings are discussed in terms of a Hough parameter estimation model of the vertical-disparity-pooling process. 1 Introduction Garding et al (1995) pointed out that computational theories of stereo vision that utilise vertical disparities can be grouped into two categories according to the scale at which they exploit those disparities. In some theories it is proposed that vertical disparity is utilised locally, by which is meant at the same spatial scale as that of the three-dimensional (3-D) depth features recovered from horizontal disparities. We will call these local-vertical-disparity theories. Theories in the second category we term regional-vertical-disparity theories because they extract certain parameters from the vertical disparity v over regions of the images, and then these parameters are used in the interpretation of 3-D structures from horizontal disparities h all over that region. We do not describe here the mathematical details underlying Garding et al's analysis. Instead we review psychophysical evidence bearing on the question of whether human stereovision implements theories of the local type, and then we report an experiment in which mechanisms for pooling of regional vertical disparity are investigated. Examples of local-vertical-disparity theories are the def theory of Koenderink and van Doom (1976) and the polar-angle-disparity theory of Weinshall (1990; see also Liu et al 1994). Both these theories can explain Ogle's (1938, 1950) induced effect, which is an illusory rotation of the visual field around a vertical axis caused by magnifying the whole of one image vertically. However, this effect can be equally well explained by regional-vertical-disparity theories and so it is of no help in deciding whether human vision uses vertical disparity locally or regionally. For deciding that question, the crucial prediction needing to be tested is as follows: purely local manipulations of v should create vivid local depth effects on a par with those created by local manipulation of h. This follows from the equivalence of changes to v and to h for local-visual-disparity theories. In other words, they create representations from the disparity vector field in such a way that changes to v should cause local perceived depth