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Weighted combination of size and disparity: a computational model for timing a ball catch


How do we time hand closure to catch a ball? Binocular disparity and optical looming provide two sources of information about an object's motion in depth, but the relative effectiveness of the two cues depends on ball size. Based on results from a virtual reality ball–catching task, we derive a simple model that uses both cues. The model is sensitive to the relative effectiveness of size and disparity and implicitly switches its response to the cue that specifies the earliest arrival and away from a cue that is lost or below threshold. We demonstrate the model's robustness by predicting the response of participants to some very unusual ball trajectories in a virtual reality task.

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Figure 1: Retinotopic and spatiotopic information for TTC judgment.
Figure 2: Changes in the timing of hand grasp when catching virtual balls.
Figure 3: Predictions from the dipole model and a modular model for the plateau conditions of Experiment 2.
Figure 4: Errors in grasp timing for the ball–catching task in Experiment 2.


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We thank Anna Plooy and Martin Smyth for their input to the second experiment and also Julie Harris, Mike Harris and Graham Schafer for incisive comments. This research was supported by the UK EPSRC GR/L18693 and GR/L16125.

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Correspondence to John P. Wann.

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Supplementary Information

Three models that combine binocular and monocular information to estimate time to contact (TTC). (a) Fixed weighting of optic size and disparity. TTC is estimated from each input and then averaged on the basis of some weighting (0 <β < 1). This approach, however, is not robust if one input is perturbed or lost, and so it will produce large errors of estimation. (b) Variable weighting of optic size and disparity. Each modular estimate is first summated (Σ) and then a cross ratio from the opposing input is used to calculate the β weightings (see Results). (c) The dipole model. Binocular and monocular motion is combined before estimating TTC. If one of the inputs is perturbed or drops out, this approach has the advantages of model (b) without the explicit iterative calculation of β weights in flight. Note that in all three models the recovery of the binocular angular subtense φ would be required for a veridical estimate of TTC from disparity, but for many natural environments relative disparity α is approximately equal to φ (see Mathematical Appendix). (GIF 26 kb)

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Rushton, S., Wann, J. Weighted combination of size and disparity: a computational model for timing a ball catch. Nat Neurosci 2, 186–190 (1999).

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