BarajasCaldwell

Introduction

Our eyes are constantly moving, even when observing a stationary object. In fact, there are two distinct types of movements: larger, sporadic scanning, called saccades; and much smaller, high frequency movements called ocular drift. Past experiments have suggested that saccades are responsible for preventing image fading on our retina— that these movements "refresh" our visual system so that we have continual neural responses to static scenes. This result has largely satisfied inquiries of the purpose of eye movements for the visual system, and many in the scientific community assume both types of eye movements serve the single purpose of preventing fading. However, Michele Rucci and Jonothan D. Victor argue that this is an oversimplification and that in particular, ocular drift serves the more profound role of amplifying higher spatial frequencies on the retina to improve visual resolution. Our work throughout this project centers on assessing this hypothesis.

Background

Literature focuses on ocular drift, which generally occurs in the period between the larger saccade movements, and is thus also referred to as "fixational" eye movement. Rucci and Victor estimate ocular drift has a mean speed of 50 minutes of arc per second, with a distribution of gaze position that disperses as time passes. An important idea of theirs is that these small motions cause fluctuations in luminance on the retina that would not be possible with a motionless eye. Since temporal fluctuations result in higher spectral power at the frequencies of the fluctuations, and since higher spectral power is associated with amplification of an image by the visual system, it follows that fixational eye movements can lead to visual amplification.

The above figure show Rucci and Victor's qualitative argument. The left plot shows higher modulations in luminance for faster eye movements, and the right plot shows their conclusion that retinal amplification increases with spatial frequency. In our project we seek to support these plots with a more quantitative foundation. An interesting result of theirs is that amplification stops increasing after about 30 cycles per degree. They note that this is around the spatial frequency that coincides with the maximum resolution of the retina itself. They also note that "natural scenes" generally have lower contrast for higher spatial frequencies and higher contrast for lower spatial frequencies. Accounting for this, they argue that amplification of higher spatial frequencies by ocular drift equalizes the power across all spatial frequencies on the retina.

Methods

Results

Photocurrent tests

In this step we examined the spectra of the photocurrent generated by the cone mosaic from the stimulus. With some simple simulations, we already saw some unexpected results. With eye movements restricted to the horizontal axis and varying sinusoidally over time, we modified the sine parameters (amplitude and frequency) so that during the simulation, the eye completed an integer number of cycles over the grating. Interestingly, no matter the parameters, the average magnitude spectrum of the photocurrent over the cone mosaic was peaked at the second fft bin (7.8125 Hz). The below plot shows values of this temporal frequency at ten different spatial frequencies, from 0 to 36 cycles per degree (scaled by the number of time samples). These temporal frequencies were found by averaging the spectra across the entire cone mosaic in the absence of noise, and with horizontal eye movements adjusted to move one cycle (bright then dark fringe) over the simulation at 4 cycles per degree. Although there is some attenuation over spatial frequency, this peak value is always very high.

This result may be related to the findings of Ehud Kaplan and Ethan Benardete that primate ganglion cells are most receptive to temporal frequencies around 8-10 Hz (1). Next, we looked at the amplification of the temporal photocurrent spectra with eye movements relative to spectra without eye movements. The plot below shows our results. We found the ratio of the spectra (between movements and no movements) at each cone on the mosaic for each of five spatial frequencies, and averaged these ratios. Our eye movements were constant over spatial frequency and tuned to move one cycle (bright then dark fringe) over the simulation at 30 degrees per cycle.

We then replicated the calculations above for each cone type individually, to determine whether different cones behaved differently. Using the same parameters, we generated the plots below.

Since the ratios are above unity for all spatial spectra, we see that eye movements definitely amplify photocurrent spectra relative to no eye movements. However, we do not see a clear relationship between increased spatial frequency and amplification, since the order of the height of the curves does not follow the order of spatial frequencies. Subsequently, we generated the same ratio plot, but isolating each type of cone individually. Below are the results for L, M, and S cones.

We see that the L and M cones follow a similar pattern to the cone mosaic as a whole, while the S cones produce steeper curves that are more closely varying. All individual cone types amplify the spectra when movements are present (since all curves are above unity), but it still certainly not clear for the cones that higher spatial frequencies are amplified more than lower spatial frequencies.

Conclusions

- It is clear that eye movements amplify temporal photocurrent spectra of a scene relative to observations of the scene without eye movements. Since the visual system is more responsive to fluctuating retinal signals than the average value of the signals, the presence of eye movements amplifies viewed scenes. - However, it is not clear whether there is a strong relationship between spatial frequency and retinal amplification. In fact, we saw that lower spatial frequencies were amplified more than higher spatial frequencies, which was the opposite of our expectation, given the ideas of Rucci and Victor.

References

Rucci, Michele, and Jonathan D. Victor. "The Unsteady Eye: An Information-processing Stage, Not a Bug." Sciencedirect.com. N.p., Apr. 2016. Web. Nov.-Dec. 2016.

Kaplan, Ehud, and Ethan Benardete. "The Dynamics of Primate Retinal Ganglion Cells." Elsevier Science, n.d. Web. 16 Dec. 2016.

ISETBIO, a software developed by Professor Brain Wandell, et al., for simulating the human visual system

Appendix 1

NOTE: the following MATLAB scripts require ISETBIO to run.

Variations on the following script were used to create the photocurrent plots on this Wiki page. Photocurrent Code

Appendix 2

Gabriel focused on simulating photocurrent spectra and ratios. Trevor focused on simulating absorption data across the cone mosaic. Both of us collaborated extensively to determine which aspects of Rucci and Victor's arguments we would investigate, and on verifying each other's findings. We formulated both the presentation and this Wiki page together, reviewing each other's contributions. We greatly thank Professor Brain Wandell for mentoring us throughout this project and being indispensable in introducing this fascinating topic to us, as well as guiding us through ISETBIO.