Exercise 2 - Direction Selectivity - Motion Energy (ME) model

Objectives:

Become familiar with the classic Motion Energy (ME) model for direction selectivity.
Consider the relation between SF and TF tuning and velocity tuning.
References:

Adelson EH, Bergen JR (1985) Spatiotemporal energy models for the perception of motion. Journal of the Optical Society of America A 2:284--299.
Download the parameter files

MEO_Gabor.moo - Motion Energy (ME) opponent model

sine_dir.stm - stimulus parameters (same as Exercise 1)

t0.rsp - response to be saved (same as Exercise 1)

Examine the contents of the parameter files
Open the model file in a text editor (or use 'more' to display it) and notice that there is a single filter object that contains the parameters to configure the spatio-temporal filter. The tilt of the filter in x-t space is determined by the values of sf and tf. The orientation preference is set by direction. The standard deviations of the Gaussian window in space and time are set by ssd and tsd, respectively.
Run the model on a direction tuning stimulus
  wm mod MEO_Gabor.moo sine_dir.stm t0.rsp tn 2048 stim_nrpt 3 outfile ex2
The diagnostic messages printed during the simulation indicate that the responses to four linear filters are being computed, via the frequency domain, for each trial.
The responses are written to ex2.nd
View the response using the nData browser (nd)
Open the data file,
  nd ex2.nd
Select the value 1 for the contrast parameter, and then choose the Tuning curve analysis. Note how this tuning curve differs from the one from the orientation-tuned simple cell in Exercise 1. (To view two tuning curves from different .nd files, consider taking a screen shot of one, or opening two nd browsers simultaneously.) This model is highly direction selective, and it appears to be a complex cell, given that the DC response is much larger than the F1 response. In fact, this is visible directly by comparing the rasters from this result that that from Exercise 1.
Spatial frequency tuning
In addition to orientation tuning, spatial frequency (SF) tuning is also a classical property of V1 neurons. Download this SF tuning stimulus,

sine_sf.stm - (same as Exercise 1)

and run the model,
  wm mod MEO_Gabor.moo sine_sf.stm t0.rsp tn 2048 stim_nrpt 3 outfile ex2_sf
and view the output,
  nd ex2_sf.nd
Examine the tuning curve (rember to select contrast as 1 to exclude the gray control trials), and compare the preferred SF value to the SF that was used to construct the filter (in the model file).
This model would definitively be classified as a complex cell, because the F1/DC ratio is far less than one at the peak of the SF tuning curve. Notice that the ratio varies substantially, with the F1 and DC responses being nearly equal at SF = 2.26 cyc/deg.
Temporal frequency tuning
It is often standard, when mapping V1 neurons with drifting gratings, to perform a test of temporal frequency (TF) tuning. Given a fixed SF, this is equivalent to varying the velocity of the stimulus. In fact, for drifting gratings, velocity = TF/SF. Download the TF tuning stimulus,

sine_tf.stm

and run the model (notice that we run it for twice as long, tn = 4096),
  wm mod MEO_Gabor.moo sine_tf.stm t0.rsp tn 4096 stim_nrpt 3 outfile ex2_tf
and view the output,
  nd ex2_tf.nd
How does the peak TF on the tuning curve compare to the relevant parameters in the model file?
The TF tuning bandwidth (e.g., width at half-height) is quite narrow, and probably unrealistic for most V1 complex DS neurons. What parameters would you change to make the bandwidth wider?
Is the model velocity tuned?
At the heart of the ME model is a linear filter that is tilted in space-time. The line running parallel to the tilt implies a particular velocity (v = tf/sf). Thus, it is reasonable to ask whether this model prefers a particular velocity of motion. One way to see the answer to this question is to change the SF of the stimulus and re-run the TF curve, to see if the peak in the TF curve has shifted, thereby remaining at the same, constant velocity.
  wm mod MEO_Gabor.moo sine_tf.stm t0.rsp tn 4096 stim_nrpt 3 sf 2.0 outfile ex2_tf2
View and compare the results (launch two nData browsers),
  nd ex2_tf.nd &

  nd ex2_tf2.nd &
The peak in the TF tuning curve for SF = 2.0 would have to be at a value that is twice that for the case where SF = 1.0, if the neuron were to have a maximal response at a particular velocity.
It turns out that Gabor filter models like this one are SF and TF tuned, and not velocity tuned. How could you modify the model to make it velocity tuned?
For one answer to this, examine the model MEO_Gabor_Rot at www.iModel.org.
EXTRA: Further visualization
Here are exmaples of ways to visualize the model filters and the raw responses of these filters.
Visualize the four 3D x,y,t filters.
  wm mod MEO_Gabor.moo sine_tf.stm t0.rsp tn 64 outfile foo filter/write_filter 5
When the simulation finishes (you can ignore the foo.dn file), you can view the filters using the following commands:
  norm3d zzz.fpe.3d 8 &

  norm3d zzz.fpo.3d 8 &

  norm3d zzz.fne.3d 8 &

  norm3d zzz.fno.3d 8 &
Click in each window and hold down the 'k' key until something appears. Use the 'j' and 'k' keys to move forward and backward in time. (press 'h' to list some of the commands in the terminal window). Note, each frame is worth 2 ms (see 'tscale' in the model file) and each pixel is worth 0.1 deg (see 'sscale' in the model file).
To examine the raw response from the four filters (preferred even and odd, and anti-preferred even and odd), and also the two non-opponent ME signals (preferrd direction ME and anti-preferred direction ME), use this response file,

t2.rsp

and run the model (e.g., here we use the direction tuning stimulus),
  wm mod MEO_Gabor.moo sine_dir.stm t2.rsp tn 1024 stim_nrpt 1 outfile ex2_raw
and view the response,
  nd ex2_raw.nd
In the nData browser, change Channel to fpe, for example, to see the output of the preferred, even filter, etc.
End of Exercise 2