Human Factors and Engineering Psychology

---------Making Gabor-----Matlab------

source:http://faculty.washington.edu/ionefine/html/MakingAGabor.html

-------function summary-----------

LINSPACE Linearly spaced vector.
    LINSPACE(X1, X2) generates a row vector of 100 linearly
    equally spaced points between X1 and X2.

    LINSPACE(X1, X2, N) generates N points between X1 and X2.
    For N < 2, LINSPACE returns X2.

Now to create a Gabor (a sinusoid windowed by a Gaussian) becomes a piece of cake. We simply multiply the two-dimensional Gaussian window by the two-dimensional Gabor.

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Making a Gabor

Here we are going to use some of the things we have learned to make a Gabor filter. These are regularly used for image processing. They are also popular as stimuli among vision scientists.

sd=0.3; % standard deviation
x=linspace(-1,1,100);
y=(1/sqrt(2*pi*sd)).*exp(-.5*((x/sd).^2));  % create a normal distribution
y=y./max(y); % scale it so it goes from 0-1

So y is a 1-d Gaussian with a standard deviation of sd=0.3. It has a minimum value of 0 and a maximum value of 1. We can plot this and see what it looks like.

plotting 1D Gaussian

plot(x, y);

create 2D Gaussian

Now we use the outer product to create a two-dimensional Gaussian filter, with a maximum value of 1 and a minimum of 0

filt=(y'*y);
disp(min(filt(:)));
disp(max(filt(:)));

  1.4962e-005

     1

view 2D Gaussian

And then we can look what that two dimensional Gaussian looks like. We are going to allow the colormap to take 256 possible values of gray. That means we want filt to vary between 1 and 256.

colormap(gray(256));
newmax=256;
newmin=1;
delta = (newmax-newmin);
scaled_filt = delta*filt + newmin;
image(scaled_filt);

Using the Gaussian filter to filter other images

We can then use this Gaussian window to filter any image we want. Let’s say we want to filter a sinusoidal grating. We actually use much the same set of tricks.

create 1-D sinusoid

sf=6; % spatial freq in cycles per image
y2=sin(x*pi*sf);
y2=scaleif(y2, 0, 1);
plot(x, y2);

ans =

     2

Create 1-D sinusoidal grating

This now gives us a 1-dimensional sinusoidal grating with a frequency of 6 cycles per image. We will scale it so it has a minimum value of 0 and a maximum value of 1. If we calculate the outer product of this sinusoid with itself we get a weird checkerboard.

img=(y2'*y2);
colormap(gray(256));
scaled_img = delta*img + newmin;
image(scaled_img);

Create 2-D sinusoid

What we want to do is calculate the outer product of the one-dimensional sinusoid with a vector of ones.

y3=ones(size(y2));
img=(y3'*y2);
colormap(gray(256))
scaled_img = delta*img + newmin;
image(scaled_img)
% Once again, img has a minimum of 0 and a maximum of 1
disp(max(img(:)))
disp(min(img(:)))

     1

     0

Create a Gabor