Observer performance and differences across conditions

On initial inspection two things are striking about the data, the first is the high accuracy with which observers are able to complete the task under a number of viewing conditions, including the least informative condition of the ACC. The second is the large individual differences between observers. Observers PBH and PS show much more accurate performance across conditions compared to observer VD, the PSE values of these observers cluster around the horizontal dashed line indicating shape constancy (Figure 4.4a and 4.4c). When these shape settings are plotted as scaling distances the data straddles the diagonal line representing a one to one relationship between scaling distance and physical viewing distance (Figure 4.4b and 4.4d). These observers’ data contrast dramatically with that of observer VD, who shows large biases in all viewing conditions except for the lidded condition (Figure 4.4e). When plotted as scaling distances it is clear that VD’s shape settings are consistent with this observer using a large underestimate of viewing distance to scale disparity across the whole distance range (Figure 4.4f). Note the difference in scale on the PSE and scaling distance plots of observer VD.

Figure 4.4: Showing the point of subjective equality (PSE) and scaling distance for each of the viewing conditions. Rows show the data from the three observers, the left column shows the PSE data and the right column the scaling distances. Error bars show 95% confidence intervals. The dashed line in both sets of graphs shows performance if observers were able to correctly estimate 3-D shape. Note the difference in the scales of the axes for observer VD.

A plot of scaling distance and physical viewing distance is typically well fit by a linear relationship (Johnston, 1991). A one to one mapping between physical viewing distance and scaling distance would result in a linear fit with a slope of one and an intercept of zero. The slope characterises the way in which the distance used for scaling changes as the physical viewing distance changes, for example, a slope less than one indicates that observers are not taking changing distance into account as much as they should, conversely, a slope greater than one indicates that observers are overcompensating for changing distance. For a linear fit with a slope of one, the intercept characterises overall bias in the distance estimates, for example, a change in the intercept of

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±x would indicate that distance is over- or under-estimated by a constant amount,

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x, across the whole distance range.

Linear fits to scaling distance data typically result in a line with a slope less than one and an intercept greater than zero, indicating that disparity-defined shape was scaled with an overestimate of near distances and an underestimate of far distances (Johnston, 1991). The point where the linear fit crosses a one to one relationship between scaling and physical distance is taken as the physical distance at which distance is estimated correctly. This has been termed the “specific” (or “abathic”) distance around which distance estimates are said to contract (Gogel & Tietz, 1973, Johnston, 1991). If shape constancy can be characterised by the extent to which near distances are overestimated and far distances underestimated, a linear fit to physical and scaling distance will rotate about the abathic distance with the extent of shape constancy. In this instance the value of the intercept is not independent of the slope, as a change in slope also results in a change in the intercept.

A least squares linear fit was made to the scaling distance data plotted against physical viewing distance and 95% confidence intervals of the slope and intercept estimated, these are shown in Figure 4.5. The slope of the fitted line is taken as a measure of depth constancy, a slope of one indicating 100% constancy and a slope of zero indicating 0% constancy (Glennerster et al., 1996, Glennerster et al., 1998). The intercept of the fitted line is typically not reported or interpreted, but it is clear that for overestimation of near distances and underestimation of far distances to occur there must be both a decrease in slope and an intercept greater than one.

Figure 4.5: Shows the slope and intercept of the least squares fit to a plot of scaling distance against physical viewing distance. Rows show the data from the three observers, the left column shows the slopes and the right column the intercepts. Error bars show 95% confidence intervals. The horizontal dashed line in both sets of graphs shows predictions for a one to one relationship between scaling distance and physical viewing distance (i.e. a slope of one and intercept of zero).

Across observers and viewing conditions slopes ranged between 0.65 and 1.1, representing 65 and 110% constancy, these values are comparable to those found in previous studies. Glennerster et al. (1996) found mean constancy across observers to be around 75% in an eye height ACC task with cylinders and dihedral angles, and near 100% with a shape matching task. In an ACC task with cylinder stimuli Glennerster et al. (1998) found constancy of 56-71% for experienced psychophysical observers and 46-62% for naïve observers, depending on stimulus size and the available distance cues. Using an ACC type task with sparse real world objects Bradshaw et al. (2000) found constancy of 76-80% depending on the viewing condition (binocular static viewing, binocular and motion parallax or monocular and motion parallax). By contrast Johnston (1991) using an ACC task with cylinder stimuli found constancy of 27 and 26% for the two observers tested (see also Johnston et al., 1993).

For observer PS the slopes of the scaling distance to physical distance relationship are very close to one for the lidded and contoured viewing conditions, for the contoured condition a slope value of one is within the 95% confidence intervals. By comparison slopes are significantly less than one for the rotated and ACC conditions, but overall performance is very high with the shallowest slope in the ACC condition showing scaling of around 80%. A similar pattern of results is found for observer VD, slopes are nearest one for the lidded and contoured condition and less than one for the remaining viewing conditions. Slopes for this observer generally show less constancy compared to those of observer PS and a slope greater than one is found in the lidded condition. This pattern of results is consistent with the lidded and contoured conditions containing the most information about object distance and shape. Observer PBH shows the opposite pattern of results to PS and VD, for this observer the ACC condition shows a slope close to one and the remaining conditions slopes show around 75-80% constancy. This is surprising as the ACC condition contains the least information about distance and shape.

Although the slopes of observers PS and VD were closest to one for the lidded and contoured conditions, which contained the most information about distance and shape, it is not clear whether a change in slope is the best way to characterise the data of observer VD. In addition to a significant change in slope across conditions this

observer also shows large shifts in shape settings in most viewing conditions, consistent with a more global underestimation of object distance across the whole range. A lack of scaling is typically characterised as the extent to which near distances are overestimated and far distances underestimated (Johnston, 1991), this is indicated by a decrease in slope and an increasingly positive intercept for the scaling distance function. Those conditions with least bias have a slope closer to one and an intercept closer to zero. This theoretical pattern of results is not consistent with shape settings of observer VD, but is generally consistent with the settings of PBH and PS. For PBH and PS those conditions with a shallower slope also have a more positive intercept (Figure 4.5).

Observer VD completed two versions of the contoured condition, in one version the raised table surface providing haptic feedback consistent with the computer rendered objects was present and in another it was absent (these are labelled “Contoured” and “Contoured no haptic (NH)” in Figures 4.4 and 4.5). It can be seen that this observer’s shape settings and scaling distances in the contoured condition with the raised table surface were far closer to veridical than when the table surface was absent. This is reflected in the global shift of shape settings toward veridical (Figure 4.4) and an increased slope of the scaling distance function (Figure 4.5). This improved performance could be due to the raised table surface providing consistent haptic feedback needed for the estimation of absolute distance from vertical gaze angle or to practice effects. The contoured condition without haptic feedback was the first condition to be completed and the contoured condition with consistent feedback the last, the intervening conditions could therefore have provided practice at the task, which improved performance, this will require further investigation.

4.4

Discussion