Comparing the Monte Carlo simulations and the psychophysical data

data

To get an idea of the level of vergence noise that would be needed to account for the bias found in observers shape settings, inverse shape settings (1/depth to height ratio) were calculated for two representative observers (HN and PBH) (Figure 3.14). Inverse shape settings represent the level of depth underestimation that would be required in order that observer’s depth to height ratio settings corresponded to a triangle with a depth to height ratio of one. These inverse shape settings can be compared to the results from the Monte Carlo simulations (compare Figure 3.14 with Figure 3.6) to assess the level of vergence noise that would be required to account for the observer’s perceptual bias. Comparison of Figure 3.14b and 3.6 suggests that the data from observer PBH can be accounted for well by the vergence noise model, the level of noise required to account the bias in this observers shape settings would be around 80-90 min arc (in half the vergence angle). This level of noise predicts the observer’s perceptual bias well across the whole distance range.

Figure 3.14: Inverse shape settings (1/depth to height ratio) for observers HN (a) and PBH (b). The key is the same for both observers. The Horizontal line in both graphs represents veridical settings. Note the difference in scale on the ordinate and abscissa for the two observers.

For observer HN the model can account less well for the data. Firstly the model does not predict a triangle with a depth to height ratio of one to be perceived as having a depth to height ratio greater than one at near distances, as seen in this observer’s data. This is because the model does not predict the overestimation of distance from vergence at any viewing distance. Whilst the overestimation of depth intervals relative to height intervals at near distances is not found in all observers, it is a consistent feature of these types of task (Glennerster et al., 1996, Johnston, 1991, Johnston, Cumming & Parker, 1993). Furthermore, in the present study observer RG made settings consistent with the overestimation of depth relative to height at all bar one distance. The model detailed above cannot account for this observer’s data. The maximum bias shown by HN is at the 110cm stimulus distance, to account for the level of bias found here would require around 70 min arc noise in half vergence. However, this level of noise does not account well for this observer’s data across the rest of the distance range. In particular, inverse shape settings seem to increase to larger depth to height ratios with decreasing distance too rapidly to be accounted for well by the model. This results in inverse depth to height ratio settings being greater than one at near distances.

It is difficult to gauge whether the level of noise required in the vergence signal to predict the magnitude an observers perceptual bias is realistic. This is because there is no clear way to estimate of the level of noise in the vergence signal accurately at present. Estimates of the amount of noise in the vergence signal are out of necessity indirect, and therefore may be unrepresentative of the true level of noise in the signal. For example, for observer PBH an 80 min arc level of noise would account for the bias in shape settings well. This corresponds to a distance range of 13.5cm (38.2- 24.7cm) at 30cm and 8055cm (8125-69.9cm) at 139cm (the nearest and furthest viewing distances for this observer). However, this does not mean that this observer would actually make this range of estimates in a distance estimation task. With this level of noise the most likely distance to have produced this noisy vergence signal at a viewing distance of 139cm is a distance of 65cm. Estimates would therefore cluster around this value, which is more realistic in terms of the level of bias demonstrated in distance estimation tasks (Viguier et al., 2001).

3.4.2

The effect of stimulus height

The present study found effects of stimulus size on depth to height ratios. Across most observers larger depth to height ratios were needed in smaller size stimuli for them to be perceived as having a depth to height ratio of one. This effect was distance dependent, with some evidence suggesting that the effect increased with increasing distance, but not across all observers. Previous studies have found effects of stimulus size on perceived depth and shape. Collett et al. (1991) had observers judge the depth between two surfaces defined by stereo and texture. They varied either distance alone, so the angular size of the stimuli decreased naturally with increasing distance, or both distance and size, so that the angular size remained constant across viewing distance. When stimuli remained constant in angular size over distance perceived depth decreased with increasing viewing distance, whereas when the stimuli changed angular size the effect of distance was diminished in most observers.

Johnston (1991) also found an effect of stimulus size in the apparently circular cylinder task. With a far 214cm viewing distance greater depth to half-height ratios were required in larger sized stimuli for them to be perceived as circular, whereas

with a near 53.5cm viewing distance greater depth to half-height ratios were needed in smaller stimuli to be perceived as circular. At an intermediate 107cm distance there was very little effect of stimulus size. Although there is some correspondence in the direction of the effect of stimulus size between the data presented here and that of Johnston (1991), the interaction between size and distance seems to differ between the studies, so the correspondence is not all that convincing.

Champion et al. (2004) investigated the effect of surface shape and stimulus size on the perceived 3-D shape of objects presented at 80cm. They found mixed results across observers and different surface shapes. There seemed to be a general trend for greater depth to be needed with larger stimuli for them to be perceived as having a depth equal to their half-height, but the reverse effect was seen with some observers for some surface shapes. Overall, there is little consistency across studies as to the effect of stimulus size on the perception of 3-D shape. The simulations detailed above do not predict any differences in the perception of shape for differently sized stimuli. At present it therefore remains unclear whether (a) consistent effects of stimulus size can be found in shape perception tasks, and whether (b) the effects of stimulus size can be predicted from any theoretical basis.