Tuesday, 25 January 2011

Identifying the Visual Information for Relative Phase

Bingham's model predicts that the information for relative phase is the relative direction of movement. The first direct test of this hypothesis was the experiment that followed on from my learning study, in which we systematically perturbed the various candidate information variables to see which affected performance in the perceptual judgement task.

I like this study a lot, if I do say so myself. It's a serious attempt to make a strong test of the model's predictions, and we invested a lot of time in the methodology. This is also that rare paper that benefited from a vigorous review process; the end result is, I think, a clear, careful, and detailed presentation of a critical result for the perception-action approach Geoff and I are developing.

Readers interested in the issue of how you can scientifically study information from an ecological perspective should certainly read the paper (Ken, that's you :); it's my go-to reference for how I believe this has to be done. The main lesson - it's hard to do this properly, but the rewards, in terms of unambiguous data, are clear.

Perturbation Methods
You may recall from my discussion of the development of the model that the dynamic characteristics of a rhythmically moving human limb were established via perturbation methods (e.g. Kay et al, 1991). This is a standard technique in dynamical systems for probing the composition and organisation of a given system, i.e. to establish what the components are and how they are arranged with respect to one another.

a. Composition
The premise of a perturbation study is simple; a given dynamical system will include some components but explicitly not include others (see also Bingham, 1988). If you perturb the value of a component, and the system does not change it's behaviour, then you have identified a component that is not part of the system at hand. Colour is a good example in human movement; altering the colour of an object rarely, if ever, affects the kinematics of a prehension movement towards that object. Colour is therefore being ignored by the prehension system (even though it may be being detected by the organism as a whole) and your model of prehension should not try to account for its effects.

On the other hand, if you perturb a variable's value and the system does respond, then you have identified something that must be included in your account of the system; in prehension a simple example is an object's size, which shapes the scaling of the hand's grip aperture as the reach is being made. Clearly, the prehension system cares about the size of objects and your dynamical systems model should therefore care too.

b. Organisation
The other important issue in dynamical systems is how these components are arranged with respect to one another. For example, Kay et al (1991) perturbed a rhythmically moving arm by abruptly changing it's motion at various points through the cycle (either speeding it up by pushing in the same direction, or slowing it down by pushing in the opposite direction). The question was, how does the system respond? If the arm returns to it's cycle at the same place in the cycle (i.e. phase) as it would have been if it had been left alone, this tells us that the arm's motion is being driven as a function of time. It's position is forced, and the system is non-autonomous. If, however, the phase is reset after the perturbation so that the arm is now in a different place than it would have been if left alone, this tells us the arm is being driven autonomously, i.e. as a function of it's own behaviour. The presence or absence of phase resetting is therefore diagnostic about how the components are coupled together.

Human rhythmic movement exhibits phase resetting and is thus autonomous, and so any driver must be made from state variables, i.e. variables which describe the behaviour of the oscillator (position, velocity or acceleration). Bingham relied on this work when formulating the model; the phase driven oscillator was therefore constructed to be autonomous (phase is simply a relation between velocity and position, two state variables). There's more than one way to build an autonomous driver, however, and while implementing perceived phase as the relative direction of motion explains the key phenomena, the evidence supporting this was still circumstantial. This study aimed to rule out the alternatives.

The other advantage here is that perturbation methods are effectively 'full-cue'. All of these displays showed coordinated rhythmic movements in which a mean relative phase was defined; we simply made different components uninformative about relative phase to see whether this had any effect on perception. Most visual psychophysics studies would have presented the candidate variables (e.g. relative position) in isolation and measured thresholds - but we aren't interested in these thresholds. What we want to know is what people detect in order to perceive relative phase.

Alternative, autonomous drivers
1. Relative Position:  the model assumes that relative phase is perceived as itself, via the detection of relative direction; however, it is possible that people perceive each phase separately and then compute the difference. Phase is a position along a spatial-temporal trajectory which lives in a space defined by position and velocity; in order to be able to perceive it, the peak amplitude and peak velocity must be well defined and stable (when you compute it, you must normalise the signal using this data). To perturb the perception of phase, we therefore disrupted this reference frame. On every half cycle, the amplitude (and thus the peak speed) of the dot was altered randomly. This meant that the reference frame from one half cycle was no longer informative about the reference frame for the next half cycle, and thus phase could not be reliably perceived. Relative direction was unaffected by this, and so relative phase was unperturbed.

Figure 1. Phase portrait (left) and time series (right) of a display where we perturbed position

2. Frequency: The position perturbation affects both the location and magnitude of peak velocity and peak amplitude. To control for this, we next kept amplitude constant and perturbed only the magnitude of peak velocity by changing the frequency over the trial.
Figure 2. Phase portrait (left) and time series (right) of a display where we perturbed frequency (we ran this in both directions)
3. Relative Speed: The second possible source of information is the relative speed; for a given amplitude, different relative phases do each have a unique relative speed signature. However, it would be trivial to make a display moving at 0° with different amplitudes which recreated the signature of, say, 180°, and it is simply not the case that anyone would mistake the relative phase. The model predicts that speed is not information, but noise on the detection of the information, but we explicitly tested a perturbation of relative speed to rule it out.
Figure 3. Phase portrait (left) and time series (right) of a display where we perturbed relative speed
Experiment 1: Perturbing 0° and 180°
We first applied these perturbations to displays with mean relative phases of 0° and 180°. The task was the 2AFC judgement task we used in the perceptual learning study, and we compared thresholds for judgements with and without the perturbations. Note that none of these perturbations affect the relative direction of motion; extensive pilot work with various displays confirmed that it was actually impossible to perturb relative direction without perturbing relative phase (a hint, in and of itself, that relative direction is the information). We predicted, therefore, that these perturbations would have no effect on judgements at 0° or 180°, because we would not be perturbing the right thing.

We had two very interesting results (Figure 2 in the paper):
  1. 7 of the 10 participants indeed showed no effect whatsoever of the perturbations. This is especially striking for the position perturbation, because it is quite dramatic; however it entirely failed to affect people's ability to visually perceive relative phase. The only autonomous alternative left is the relative direction of motion.
  2. 3 of the 10 were entirely perturbed by the position perturbation (and not by the others). Thresholds jumped enormously, and one participant was effectively entirely at chance. 
This demonstrates two things - it confirms that the perturbations are selective in their effects and not simply making the task too hard, and second, it suggests that only  seven people were using relative direction to perceive relative phase. This was entirely unexpected, although with hindsight it made sense; see below for some thoughts.
Experiment 2: Perturbing Trained Perceivers of 90°
The first version of the previous learning study had provided us with 8 expert perceivers of 90°. The model actually makes no specific predictions about how people learn, although as I discussed in the last post the most likely scenario is that people begin using a different information variable. Relative direction is always variable and noisy at 90°, and improved detection of a noisy variable still results in noisy performance; plus learning had not generalised to 180°, which it should have if learning simply entailed lower thresholds for relative direction.

We therefore compared thresholds for judgements of 90° with the perturbations and without. The results are in Figure 4 (adapted from the paper)
Figure 4. Thresholds for judgements of 0°, 180° (by the 7 unaffected people) and 90° (by the 8 trained participants) for the four perturbation conditions
The trained participants completely lost their ability to perceive 90° under the position perturbation; thresholds were high, as was variability. The frequency perturbation also affected perception of 90°, but the effect was only about half the size. The speed perturbation had no effect. Learning to perceive 90° therefore entails learning to perceive a new variable, relative position, which requires a stable reference frame to be defined.

Some thoughts
The position perturbation affected all the trained participants; they were therefore all using the same information. The explicit training clearly pushed performance towards a single solution. The individual differences seen at 0° and 180° may therefore be the result of incomplete learning. Relative position is clearly 'good enough' in the absence of a perturbation, and even though relative direction is the better solution (it is robust in the face of all the perturbations, for example) people may only learn to use it once exposed to conditions when their current solution breaks (i.e. when the scope of their solution is exposed as inadequate). This is certainly something I will be pursuing experimentally in the near future.

The perturbation methodology was extremely informative, and it's success validates our approach of treating perceptual information as a component of a dynamical system. Relative phase was always defined 'in the world', and specified by the relative direction of motion, even under the perturbations: failure to perceive relative phase under a given perturbation therefore told us precisely what was being used as information.

Bingham, G. P. (1988). Task-specific devices and the perceptual bottleneck. Human Movement Science, 7, 225-264. Download

Kay, B. A., Saltzman, E. L., & Kelso, J. A. S. (1991). Steady-state and perturbed rhythmical movements: A dynamical analysis. Journal of Experimental Psychology: Human Perception and Performance, 17(1), 183–197.DOI
Wilson, A. D., & Bingham, G. P. (2008). Identifying the information for the visual perception of relative phase Perception & Psychophysics, 70 (3), 465-476 DOI: 10.3758/PP.70.3.465 Download

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