Question

I would like to compute the Covariance Matrix of the image below. Pixel based. That is considering each Black Pixel of the Disks as vectors.

While the units below are in centimeter, there are 32 pixels per cm on the screen I am using.

Ahead of the Covariance Matrix computation itself, I can`t figure out the way to obtain all the pixels vector.

frmXY = {{6.59, 1.59}, {33.41, 28.41}};

stim = {{10.85, 21.91, 0.97}, {16.8, 5.26, 0.97}, {11.78, 7.11, 0.97}, 
        {12.64, 14.13, 0.97`}, {20.24, 16.16, 0.97}, {29.51, 8.06,1.53}, 
        {22.42, 5.78, 1.53}, {27.13, 16.47, 1.53}}


Graphics[{EdgeForm[Thick],White, Rectangle @@ frmXY, Black,
          Disk @@@ (stim /. {a_, b_, c_} :> {{a, b}, c})}, ImageSize -> 300]

Answer 1

It is not clear from your question as to what constitutes the random variable that describes your model/system and I don’t understand what it is that you’re trying to take the covariance matrix of.

However, here’s a simple example showing how to obtain the covariance matrix and compute the eigenvalues and eigenvectors (basically, reproduce your first plot).

list = RandomReal[
   MultinormalDistribution[{0, 0}, {{6, 3}, {3, 3}}], {5000}];
sampleCov = Covariance@list;
{eigValues, eigVectors} = Eigensystem@sampleCov;

Show[ListPlot@list, 
 Graphics[{Red, Arrowheads[0.03], 
   Arrow[{{0, 0}, #}] & /@ (eigValues eigVectors)}]]