Opponency, Quadrature and Displacement Tuning in Two-Frame Motion

Nicolas Heess¹ and Wyeth Bair²

¹Neuroinformatics DTC, School of Informatics, Univ of Edinburgh, Edingburgh, UK
²Dept. Physiology, Anatomy and Genetics, Univ of Oxford, Oxford UK
wyeth(dot)bair(at)dpag(dot)ox(dot)ac(dot)uk

Summary

The visual motion literature from about 1985 to 2010 supports the idea that a preference for 1/4 cycle displacement in 2-flash apparent motion displays arises from directional mechanisms that use quadrature filters. Here, we present models and stimuli to demonstrate that quadrature does not lead to a preference for 1/4 cycle displacement in mainstream motion models, such as the motion energy model (Adelson and Bergen, 1985). Instead, an important factor is motion opponency, the subtraction of two oppositely tuned motion signals, which does lead to a preference for 1/4 cycle in 2-flash stimuli for a broad class of model (Heess and Bair, submitted).

Visual Stimulus

The 2-flash grating stimulus consists of two brief flashes of a patch of sinusoidal grating (Nakayama and Silverman, 1985). In the second flash, a phase offset is added to the spatial phase of the grating. To view this stimulus, click the button below to launch the iModel stimulus viewer. Then click Play or scroll through frames manually to see the sinusoidal stimulus flash twice. The second flash has a 1/4 cycle (90 deg) phase offset.

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Model Results

We tested an opponent motion enery (ME) model, MEO_Gabor.s2t1, using the 2-fash stimulus with a variable phase offset. We recorded the intermediate responses of the four linear filters (fpe, fpo, fae, fao), the two non-opponent motion energy signals (mep, mea), the opponent signal (meopp), and the final spikes (see MEO_Gabor for a diagram of these signals). To examine these outputs, click the following button to launch the iModel data viewer, and note the steps below:

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1. In the data viewer, select the opponent ME response (meopp channel) and select the Tuning Curve analysis format. This shows that the integral over time of the responses to the 2-flash stimulus is maximum for a 1/4 cycle (90 deg) displacement.

2. However, select the preferred ME response (mep channel) and the Tuning Curve analysis format. The displacement tuning curve does not peak at 1/4 cycle, demonstrating that the quadrature non-opponent ME unit does not have a preference for a 1/4 cycle jump, in spite of it being a quadrature model. Also, note that the tuning curve for the mea, the anti-preferred ME response, is mirrored about the y-axis, relative to mep. This demonstrates that it is the opponent subtraction of these two signals, not the underlying quadrature architecture, that leads to the opponent model having the 1/4 cycle preference for 2-flash gratings.

Models

The following models are relevant to the points here:

• MEO_Gabor - An opponent Gabor-filter motion energy model.
• ME_Gabor - To be added. A non-opponent Gabor-filter motion energy model.
• LN_Opp_RandFilt - To be added. An opponent model based on a randomly generated linear filter.

References

• Heess N, Bair W (submitted) Direction opponency, not quadrature, is key to the 1/4 cycle preference for apparent motion in the Motion Energy Model.

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• Nakayama K, Silverman GH (1985) Detection and discrimination of sinusoidal grating displacements. J Opt Soc Am A 2:267--274.
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• Watson AB, Ahumada AJ Jr (1983) A look at motion in the frequency domain. NASA Technical Memorandum 84352:1--10.
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