Are systematic distortions of perceived shape and distance examples of a

It has been suggested that the overestimation of near distances and underestimation of far distances, typically described in terms of a SDT, may simply represent a ‘contraction bias’ whereby in conditions of uncertainty observers responses regress to the centre of an available response range, which has the result of reducing average error (Mon-Williams & Tresilian, 1999). More specifically this is what Poulton (1989) would term a ‘response contraction bias’. The response contraction bias occurs when observers have a limited range of responses available with a known centre or range, under these conditions they tend to make responses which are biased toward

the centre of the available range (Poulton, 1989). In this interpretation the systematic distortions demonstrated in distance and depth perception tasks should not be taken as a failure of vergence to accurately determine object distance. Instead distance might be accurately estimated from vergence and used to scale horizontal disparity for the estimation of depth, but observer’s responses regarding distance or depth might be biased to the middle of the available response range (Mon-Williams & Tresilian, 1999, Mon-Williams, Tresilian & Roberts, 2000).

In a direct distance estimation task it is clear to see how a contraction bias could operate to produce results consistent with the SDT if an observer has an estimate of the response range. However, this interpretation is inconsistent with studies that have shown near distances to be estimated reasonably accurately (e.g. Viguier et al., 2001). It is less clear how the results of 3-D shape judgement tasks could be explained by a contraction bias. The results of shape judgement tasks such as the ACC are consistent with a contraction bias in distance estimates. Contraction biases act on the unit of response (Poulton, 1989), in the case of shape judgement tasks this would cause observers to bias their estimates and decisions toward an intermediate shape within the range3_{. Unless observers were presented with a range of shapes centred on a} theoretically expected bias in perceived shape at each distance within the range, it is difficult to see how responses in a shape judgment task could result in a pattern of results consistent with a contraction bias in distance estimates.

It is also hard to reconcile a contraction bias explanation with the notion that observers are completing a task on the basis of perceived distance or shape. A contraction bias suggests that observers effectively disregard perceived distance and shape in favour of biasing their judgements to the middle of the available range. This is not representative of observer’s performance in experimental tasks, or observer’s subjective reports of how they complete these tasks (Figure 3.1). Many shape judgement tasks are also blocked by distance in order to reduced the effects of screen cues to distance/depth (Watt et al., 2005a), ‘blocking’ distance estimates is known to

3 _{Here “shape” could refer to un-scaled retinal disparity, depth as compared to width/height or} a higher-level estimate of shape such as curvature, depending on how you wish to interpret an observer’s completion of the task.

eliminate the effects of the contraction bias (Mon-Williams & Tresilian, 1999, Poulton, 1989).

Figure 3.1: Example psychometric function for an observer performing the apparently circular cylinder task in the ‘Lidded’ condition of the experiment reported in Chapter 4. In brief, stimuli were presented on four interleaved adaptive staircases, with a total of 262 trials. The depth to width ratio of the stimulus is shown on the abscissa and the proportion of ‘stretched in depth’ responses on the ordinate. The 0.5 performance level (PSE) indicates the depth to width ratio needed for the observer to perceive the stimuli as circular. The range of the stimuli in this instance was not ‘centred’ around the observers PSE. It is immediately clear that observers are not simply biasing their responses to the middle of the available response range, despite remaining subjectively unsure of the accuracy of their responses. The value of the PSE was a depth to width ratio of 1.03 (upper 95% confidence interval 1.06, lower 95% confidence interval 1.02) and by comparison the centre of the stimulus range was 1.5. This suggests that observers are performing these types of task on the basis of perceived shape.

A further prediction the contraction bias makes is that as the available cues to distance increase the contraction bias should decrease, because more cues are available from which to estimate distance (Tresilian et al., 1999). However, this is also true of explanations in terms of the traditional specific distance tendency (Gogel, 1969,

Gogel & Tietz, 1973). It is possible that similar results to a contraction bias could be produced if observers built up an estimate of the average object distance during the course of the experiment, and that this acted to bias perceived distance and shape. This would be somewhat similar to the action of a distance prior (Yang & Purves, 2003), but one learnt over the course of the experiment. The role of prior information about distance is discussed in a later section. For now it seems reasonable to assume that part of the bias in distance and shape estimates may be due to the way in which distance is estimated from sensory information about the vergence state of the eyes.