Question

I have an RGB image, call it img, represented as a double array with size (100,200,3)

I have a binary mask (call it mask), that’s a logical array with size (100,200).

I want to know the mean pixel value for the masked region.
I also want to know the complete (3×3) covariance matrix for pixel values in the region.

Now, if this were a single channel (as opposed to 3 channel) image, I could simply do:

mean(img(mask(:)))
std(img(mask(:)))

It’s straight forward to do a similar operation in a loop for each channel, pulling out the values, then building up a large 3xN matrix (where N is the number of “trues” in mask and finally, operating on that matrix with mean and cov. Curious if there’s a way to do it without a loop. I’m not seeing it.

Answer 1

Replicate your mask into the third dimension and apply it like normal. Then simply reshape the vector output into a matrix with a row for each pixel in the mask, and a column for each color channel. Here is an example using a built-in image:

% Load image
X = imread(('board.tif'));
X_size = size(X);

% Make mask
mask = zeros(X_size(1:2));
mask(250:251, 100:102) = 1;
mask = repmat(mask, [1 1 X_size(3)]);
mask = logical(mask);

% Apply mask to image
X_data = X(mask);
X_data = reshape(X_data, [length(X_data)/X_size(3) X_size(3)]);

% Compute stats
mean(X_data)
cov(double(X_data))

Now, just to check, if we inspect the first pixel inside our mask in the original image X

>> X(250, 100, :)

ans(:,:,1) =

  144


ans(:,:,2) =

  125


ans(:,:,3) =

  123

it should equal the first row in X_data:

>> X_data

X_data =

  144  125  123
  128  138  135
  180  186  184
   60   68   70
   38   42   26
   55   49   44