PROCEDIMIENTO 1 OBJETIVOS:

There are a number of stages in the estimation of distance from the vergence state of the eyes at which bias and uncertainty could be introduced; these are schematically illustrated in Figure 3.2. Bias and uncertainty could be introduced at any one of these stages. Discussion will focus on three possible ways in which estimated distance might be biased, for the purposes of this discussion its will be assumed that the estimated distance is reported correctly,

!

ˆ

D =D_R, i.e. there is no contraction bias operating. The first way in which estimated distance might be biased is if the physical vergence state of the eyes

!

"V was biased away from the correct vergence state needed

for object fixation

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"F. The brain’s estimate of the vergence state of the eyes

!

ˆ

" could be correct, such that

!

ˆ

" ="V, but due to the physical misconvergence of the eyes this

would result a biased estimate of object distance

!

D_F "D ˆ =D_V. An example of this type of bias is the case where the dark vergence state biases the physical convergence state of the eyes resulting in a fixation disparity (Owens & Liebowitz, 1976).

Figure 3.2: Schematic diagram showing the estimation of distance from the vergence state of the eyes. The observer is required to fixate an object

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T at a distance

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DF this defines the vergence angle

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"F. The physical angle of convergence

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"V, which corresponds to a distance of

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D_V, may or may not correspond to the vergence angle needed for correct fixation. The brains estimate of the physical state of convergence is represented by

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ˆ

" . Given this vergence estimate an estimate of object distance

!

ˆ

D can be made. This distance estimate is then reported through a certain means of response e.g. verbally or manually, this reported distance estimate is represented by

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DR.

It is likely that some of the disparities present within experimental stimuli for shape and distance judgement tasks would not be fusible for the observer. However, it is unlikely that physical misconvergence of the eyes could account for the biases found in estimates of distance and 3-D shape. The misconvergence required to account for the biases would result in the two eyes’ images becoming diplopic such that the observer would be unable to do the task. For example, Johnston (1991) got observers to fixate a cross on the median plane at the same viewing distance as the stereoscopic stimulus in order to ensure correct vergence demand. If it is assumed that (1) all error in set shape is due to observers misestimating object distance and (2) observers estimated distance solely from the vergence state of the eyes, which were misconverged at this incorrect distance, it is possible to get an estimate of the tolerable fixation disparity that would be required for the observer to misconverge at

the scaling distance yet still see the fixation cross as fused4, as was required in the experiment.

The value of fixation disparity required in Johnston (1991) is approximately 136 min arc for the near viewing distance (53.5cm) and approximately 117 min arc at the far viewing distance (214cm). These values are clearly much larger than the

!

"6 min arc fixation disparity tolerable with foveal fixation of a target (Howard, 2002). Qualitatively different impressions of depth can be gained with diplopia and observers are known to feel uncertain in making shape settings during tasks such as the ACC (Todd & Norman, 2003), but observers do not generally experience diplopia whilst competing experimental tasks and report being able to complete these tasks on the basis of perceived shape. This suggests that they make their judgements about shape on well-fused images, and are therefore converged on the object to within Panum’s fusional area whilst doing the task.

A second possible source of bias could be introduced if the eyes were correctly converged on the stimulus such that

!

"V ="F, but the brain’s estimate of the vergence state

!

ˆ

" was biased such that

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ˆ

"#"_V, this would result in bias in the perceived distance

of the stimulus

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ˆ

D "D_F. This type of bias could be introduced if dark vergence acted to bias the vergence estimate, rather than the physical convergence state of the eyes. As a final example, consider a case where the eyes were correctly converged on the object and the brain estimated this vergence state correctly, such that

!

ˆ

" ="_V ="_F, yet estimated object distance was different to the physical distance of the object,

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ˆ D "D_F. In a Bayesian framework this type of bias could result from the mapping that relates the vergence state to a distance estimate, as embodied in the likelihood function, or the combination of sensory information about object distance with prior distance information (Mamassian et al., 2002).

4 _{This was accomplished by calculating the difference between the vergence angle for} fixation at the distance of the fixation cross and the vergence angle for fixation at the scaling distance.

3.1.9

The precision of vergence: distance estimation as Bayesian