Exercise

The goal of this exercise is to program a 1D retinotopic map of disparity energy filters with preferred disparity of 0. You will use the model proposed by Ohzawa and Freeman (see figure below). More specifically, you should follow the steps below:

1- Generate the right and left images of a bar two pixel wide with a horizontal disparity of 2 pixels and a pixel value of 1. Each image should be 1x128, with a background pixel value of 0.

2- Program the 4 different types of receptive fields for the simple cells shown on the figure (left side of panel b). Use Gabor filters 1x128 pixels wide with parameters: s=5, 1/w=10 pixels per cycle

The first receptive field shown on the figure corresponds to the following equation

S(x)=exp(-x^2/(2s²))cos(w2px)

The other 3 are just variations of this equation.

3- Convolve the right and left image with the receptive fields of the simple cells (using Fourier transforms) and pass it through a nonlinearity consisting of a rectified square function (DO NOT MODEL THE INHIBITION BETWEEN SIMPLE CELLS SHOWN ON THE FIGURE). This should result in four maps, each 1x128, corresponding to the four types of simple cells.

4- Combine the response of the simple cells to obtain the response of the complex cells.

5- Plot the activity of the 128 complex cells.

Repeat all this steps for a range of shift from –10 to 10 in step of 1 to obtain the tuning curves of one representative complex cell to disparity. If you’re not getting a bell shape tuning curve centered on zero, go back to step 1 and start from scratch!

6- How would you generate a complex cell centered on a non zero disparity? Generate one such cell.

Tip: when you inverse Fourier transform, the image may turned out to be complex. This is due to numerical approximation in matlab, i.e., the imaginary part are in fact very close to zero (<1e-3). Check that this is the case and use only the real part of the inverse Fourier transform.