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Gogel (1969) suggested that in the face of ambiguous information about target distance, as is typical of most psychophysical studies, the visual system’s estimate of distance might shift toward some default value, this was termed the ‘specific distance tendency’ (SDT). In this framework, as the information available to an observer from which to estimate distance is decreased, estimates shift toward a specific or intermediate distance value (Gogel & Tietz, 1973). As a consequence of this near distances are overestimated and far distances are underestimated. The distance around which estimates are thought to contract was considered to be stable for a given observer in a given viewing situation, but variable over different observers and for the same observer in different viewing environments, where the availability and quality of visual cues may vary.

Gogel and Tietz (1973) used an illusory motion parallax task and verbal distance estimation to investigate the SDT. In the illusory motion parallax task observers slid their head laterally side to side whilst fixating a point of light presented at a range of distances (30cm to 8.83m) in an otherwise dark environment. In this viewing situation illusory motion of the point of light is predicted if the observers accurately fixate and track the light but misestimate its distance. If the light’s distance is underestimated it will be perceived as moving laterally with the movement of the head, whereas if its distance is overestimated it will be perceived as moving laterally against the movement of the head. The light will only appear as stationary if its estimated distance is the same as the distance of fixation. Two groups completed the motion parallax and distance estimation tasks, one group with monocular vision and one group with binocular vision.

In the motion parallax task observers more frequently perceived motion of the light against movement of the head at nearer distances and motion of the light with movement of the head at further distances. The distance at which the frequency of observers’ responses to movement of the light were equally ‘with’ and ‘against’ their head movement was interpreted as the distance at which perceived distance was equal to the distance of object fixation. This was approximately 3m for monocular viewing

and 5m for binocular viewing. If the rationale of the task is accepted, the results suggest that near distances are overestimated and far distances underestimated, but differentially so for monocular and binocular viewing. It is also worth noting that the inferred abathic distance differs greatly to the 80cm abathic distance inferred in 3-D shape judgement tasks (Glennerster et al., 1996, Johnston, 1991)

In contrast to the motion parallax task, verbal estimates of distance provide mixed evidence for the SDT. Gogel and Tietz (1973) report both un-calibrated and calibrated verbal distance estimates, the un-calibrated distance estimates are the raw distance estimates reported by the observer, whereas the calibrated distance estimates have been corrected by a function fitted to observers’ verbal estimates of distance and physical distance, as determined under sparse fully illuminated binocular viewing. There are important differences between the two measures so both are discussed. The authors base their conclusions on median data as the distributions of estimated distance are skewed. For monocular viewing the calibrated distance estimates indicate that distances under

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"2m are overestimated and distances over

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"2m are underestimated. The uncalibrated distance estimates indicate that distances greater than

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"2m are underestimated, but the overestimation of near distances is inconsistent.

For binocular viewing the calibrated distance estimates indicate that distances over

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"2m are underestimated, with a small overestimation of nearer distances. In contrast, the uncalibrated distance estimates indicate that distances >1m are underestimated but distances <1m are estimated accurately. The assumption underlying the calibration procedure is that distances are veridically perceived in the ‘full cue’ calibration condition and that any errors present in this condition result from converting an accurately perceived distance into a verbal distance estimate (Gogel, 1969, Gogel & Tietz, 1973). This is analogous to the observer having an incorrect criterion for the unit of measurement, for example if an observer underestimated the length of a metre all distance estimates reported in metres would be underestimated by a fixed proportion.

Although the criterion an observer has in mind for a particular unit of measurement is an interesting issue, comparison of the calibrated and non-calibrated data show that the use of the calibration function acts to add additional bias into observers’ distance

estimates (e.g. Gogel, 1969, Gogel & Tietz, 1973). It is a strong assumption to suggest that all error in the calibration condition is due to observers having an incorrect criterion for the unit of measurement used for verbal report. Bias might be introduced at a number of stages during processing and could in part be due to the nature of the viewing geometry itself. Occam’s razor would suggest that as the use of the calibration procedure acts to add additional bias into observer’s distance estimates; the use of uncalibrated distance estimates would be the more appropriate measure of perceived distance.

It is also unclear whether the assumptions underlying interpretation of the data from the motion parallax task in terms of pure distance misestimation are valid. To be interpreted in terms of misestimated distance alone, observers would need to have accurately fixated the target and accurately tracked its position whilst making lateral head movements. They would also need to have accurate knowledge of the distance their head had moved. Illusory movement of the point of light would be predicted if any of these assumptions were not met, as was recognised by Gogel and Tietz (1973). This makes it difficult to assume that the task is a direct measure of misestimated viewing distance. The results of these tasks are therefore unclear as to biases that may exist in the estimation of distance from vergence information.

In a distance estimation task Viguier et al. (2001) got observers to set the distance of an LED cursor to be equal to, half that of, or double that of, a reference LED. The reference was placed at a range of distances along the median plane (between 20- 80cm, depending on the task) and the cursor was positioned along a line parallel and 4cm to the right of the median plane. Both were presented at eye height and across all tasks the reference LED subtended a constant angular size and had equal luminance across the distances tested, whereas the cursor’s angular size and luminance varied appropriately with distance. Both the cursor and reference were viewable, meaning that relative disparity information was available for setting the cursor’s distance. In a fourth condition equal distance settings were made but without a concurrently seen reference. In this condition the reference was presented alone for five seconds and then turned off for five seconds, before the cursor was presented for the distance setting. This dark interval was used to allow vergence to adopt a resting state between the presentation of the reference and cursor to eliminate any relative disparity

information. Finally, in a fifth condition, the reference was presented alone and oral distance estimates were made.

With concurrent viewing of the cursor and reference equal distance settings were highly accurate across the whole distance range, reflecting the availability of relative disparity information. However, half distance settings were overestimated at near distances and underestimated at far distances, and all double distance settings were underestimated. Verbal responses underestimated all reference distances and this tendency increased as the reference distance increased. The authors interpreted the underestimation of distances in the double, half and verbal judgment tasks as indicating that observers used an egocentric reference of

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"10cm from themselves from which to judge distances. This reference corresponds to the maximum possible vergence angle (Collewijn & Erkelens, 1990). This fits the data but it is unclear why the visual system would adopt such a strategy in the face of inconsistent feedback during tasks such as prehension and conflicting information from other visual cues. Furthermore, with more than one target in the scene clear biases in the estimated distance of the target object would be expected from previous data (Foley, 1985).

Importantly with sequential presentation of the cursor and reference distance settings were accurate up to 40cm but progressively underestimated at 60 and 80cm. Accurate estimation of near distances is what would be expected from the geometry of vergence. Eye movements were tracked for four subjects during a 3 second fixation of the cursor and reference LED’s. A clear inversely proportional relationship between the vergence angle and fixation distance was seen as would be predicted from the geometry of vergence in the experimental task. This suggests that observers were accurately fixating the target across the distance range used. In general the precision of distance estimates decreased as the reference distance increased across all tasks. Accurate perception of near distances when vergence is the predominant distance cue has been reported in a number of other studies studies.

Swenson (1932) got observers to manually estimate the perceived distance of a binocularly viewed target along the median plane with a movable pointer positioned below the stimuli. Target luminance and angular size were kept constant. At each of the three near distances tested (25, 30 and 40cm) manual distance estimates were

highly accurate with mean errors <2mm. Mon-Williams and Tresilian (1999) got observers manually to judge the distance to a binocularly viewed single point light source in an otherwise dark environment. The light source was presented at a fixed presentation distance directly in line with the right eye. Vergence specified distance between 20 and 60cm was manipulated with ophthalmic prisms placed in front of the left eye.

A regression of perceived distance on vergence specified distance suggested that observers tended to overestimate near distances and underestimate far distances. This interpretation of the results can however be questioned. Both base in and out prisms were used to manipulate vergence specified distance, this means that the (fixed) distance of the point light source was within the vergence specified distance range. Vergence specified distance therefore conflicted with distance information from other visual cues, such as accommodation. In a cue conflict situation such as this estimated distance has been shown to be a compromise between that signalled by the conflicting visual cues (Watt et al., 2005a), as would be predicted from models of cue combination (Landy et al., 1995). Cue conflicts could therefore explain the apparent contraction in distance estimates.

Tresilian, Mon-Williams and Kelly (1999) demonstrated similar results in a study that used prisms to manipulate vergence specified distance within a viewing box. Distance estimation was investigated in a range of viewing conditions designed to assess the role of additional visual cues in the surroundings (rich cue, reduced cue and darkness), changing angular size of the target object, and monocular versus binocular viewing. Targets were large rectangles of black card during viewing in the light and luminous tubing when viewed in the dark, with the exception of one dark condition in which a point light source was used. All targets were viewed in line with the right eye, which allowed vergence specified distance to be manipulated with prisms in front of the left eye in some conditions. Objects were placed between 25/30cm and 100cm (depending on condition) and distance was manually estimated using an indicator stick on the outside of the viewing box.

A strong linear relationship between perceived and physical distance was found across all conditions. In addition, base in prisms were shown to increase perceived

distance and base out prisms to decrease perceived distance, as would be expected by the prismatic viewing geometry. The effect of the prisms increased as the available visual cues decreased, which would be predicted on the basis that vergence information now conflicted with fewer visual cues. This cue conflict was evident in the point light condition, in which the target’s physical distance was fixed at 50cm, but vergence specified distance was manipulated using prisms. Here overestimation of near distances and underestimation of far distances was found. Discussion will focus on the conditions where no prisms were used, as these contained no cue conflicts.

In the rich cue condition with angular size varying appropriately with target distance, estimated distance was highly accurate. When angular size was removed as a cue to distance or targets were viewed in the reduced cue environment there was a general tendency for further distances to be underestimated, although estimated distance remained reasonably accurate under most cue conditions. When viewing luminous tube targets in the dark with angular size as a cue, distance estimates were more variable compared to the lit conditions and distances up to

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"80cm were slightly overestimated. When these stimuli were viewed monocularly in the dark and changing angular size was the only cue to object distance, far distances were underestimated and near distances were overestimated but to a smaller amount. These data suggest that in natural viewing conditions vergence can provide a valuable source of distance information.

Foley and Held (1972) got observers to manually estimate the position of (a) a point light source viewed in the dark and (b) short plastic rods viewed in the light, with an unseen hand. The plastic rods were viewed in the light on a gridline surface positioned 3cm below eye level and two context ‘tack’ objects were present, so multiple cues such as perspective, accommodation and relative size were available. The point light source was produced by viewing two laterally separated lights, presented at a fixed distance of 75cm, 1.5cm below eye level, through polarising filters in front of each light and eye. The point light sources were presented at eye level and appeared at the same height as the tops of the rods resulting in vergence being the predominant cue to distance. Targets appeared at distances up to 36cm along either the median plane or a plane running 16.2 degrees to the right or left of the median plane.

In both viewing conditions, along each viewing plane, observers tended to overestimate target distance; this overestimation was much greater (up to 25cm) for the point light source viewed in the dark. As before, the overestimation of the point light source’s distance is likely to be related to conflicts between vergence and other visual cues. It is less clear why observers consistently overestimated distance by up to

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"11cm in the multi-cue condition where there were no cue conflicts. Manual estimation of distance has been found to be highly accurate for distances up to 50cm in other studies using a rich cues consistent environment (Mon-Williams & Tresilian, 1999, Tresilian et al., 1999).

3.1.3

Making links between the misestimation of distance and the