Binocular Disparity Energy (BDE) models

Objectives

To study a model of V1 cells with binocular interactions.

References:

Ohzawa I, DeAngelis GA, Freeman RD (1990) Stereoscopic Depth Discrimination in the Visual Cortex: Neurons Ideally Suited as Disparity Detectors. Science 239:1047-1051.

The model used here has documentation on www.iModel.org: BDE_Gabor

V1 is the first stage where neurons receive inputs from both left and right eyes. This gives rise to a novel type of response property, binocular disparity selectivity.
The classical model of binocular disparity selectivity is a spatiotemporal filter model much like the V1 ME model that you have already been introduced to. This is called the binocular disparity energy (BDE) model. This classical version of this model is available on the iModel website as BDE_Gabor. Instead of combining signals from subunits with RFs that differ in spatial RF phase, signals are combined from subunits that are in different eyes. These subunits may have a spatial phase difference, giving rise to different types of disparity selectivity.
Open the model parameter file from the BDE_Gabor model homepage linked above. There are three additional parameters used with model type binoc_filter for generating disparity selective units:
   phase_shift   0        # Spatial phase difference between input to each eye.
   phase_1       0        # Spatial phase of the cosine for first left-eye Gabor 
                          # filter
   binoc_nonlin  halfsq   # Type of output nonlinearity -- squaring or 
                          # half-squaring
The three additional parameters right_sign, simp_rect and simp_thresh are used in a modified disparity energy model proposed by Read et al. that will not be covered in this exercise.
Characterization with drifting gratings
As you have done for the motion energy model, you can characterize the BDE model with sinusoidal gratings. For binocular models, you can display stimuli to the left eye, the right eye, or both at the same time. There are additional parameters to set for generating a binocular stimulus:
  stim_form           3d_b    # Specifies a binocular stimulus
  stim_monocular      left    # Which eye(s) the stimulus is presented in
                              # ['left', 'right', 'both']
In the classical BDE model, subunits in the left and right eyes have almost identical spatiotemporal properties (with the exception of RF spatial phase), and so the preferred stimulus when driving each eye monocularly is the same for each eye.
Now try testing binocular disparity selectivity in the model. Run the stimulus sine_phase_bi.stm to test tuning for phase disparity in the BDE_Gabor model. Set the SF and TF parameters as appropriate for the Gabor filter parameters in the model file. Change the phase_shift in the model by steps of 90 degrees (between -180 to 180 degrees) and run disparity tuning curves for these variations. Models with with +90 and -90 degree disparity tuning are referred to as near and far cells since they respond best to stimuli either in front of or behind the plane of fixation.
Generate a direction tuning curve for the BDE_Gabor model with gratings presented monocularly (left or right eye) and binocularly. For monocular tuning curves you will need to edit the sine_dir stimulus to add the additional parameters for binocular stimuli. Use the response file t.rsp. Compare the responses to monocular vs. binocular stimulation. Do the responses of the BDE_Gabor model to monocular and binocular stimulation match what you would expect from binocular V1 cells?
Characterization with random dot stereograms
Instead of sinusoidal gratings, random dot stereograms are typically used to test disparity-sensitive visual neurons. RDS stimuli have often been used in psychophysical studies of stereopsis, and so to understand the neuronal basis of depth perception it is important to study visual neurons using the same stimuli.
In the rds stimulus, a patch of random dots is shifted horizontally in the right eye relative to the same dot pattern in the left eye. To see this most easily in the stimulus viewer link above, pause the movie and step through each stimulus to see the patch shifting position. Dots can be all one luminance or both black and white (bipolar). The default version of this stimulus uses correlated random dots, where the luminance of the dots in each eye is matched. The stimulus can also use anti-correlated random dots, where black dots in one eye are white in the other eye, and vice versa. If you are able to fuse the two stimulus frames, you may do so and see if the patch appears in depth when there is a positional disparity.
Run disparity tuning curves by downloading the RDS stimulus rds_dwell.stm and uploading it to your iModel account. You can edit this file, or set the following parameter values as custom parameters in the simulation:

dotdens 25.0
dotsize 1.0
dwell 2

Run disparity tuning curves for both correlated and anti-correlated dots by setting values of the parameter dotcorr to 1 and -1.
How are the tuning curves related to each other? If the BDE_Gabor model is a good model of a V1 disparity-selective neuron, what does that imply about the role of these neurons in steroscopic depth perception, given these results?