Basic FreeMat/MATLAB syntax - dimension error

Question

I am using FreeMat, and I have an RGB picture which is a 3D matrix contains the columns and rows of the pictures and the RGB values for each pixel.

Since there is not an intrinsic function to convert RGB picture to YIQ, I have implement one. I came up with this code:

Assume I have a 3D array, image_rgb:

matrix = [0.299 0.587 0.114;
0.596 -0.274 -0.322;
0.211 -0.523 0.312];
row = 1:length(image_rgb(:,1,1));
col = 1:length(image_rgb(1,:,1));
p = image_rgb(row,col,:);

%Here I have the problem
mage_yiq(row,col,:) = matrix*image_rgb(row,col,:);

max_y = max (max(image_yiq(:,:,1)));
max_i = max (max(image_yiq(:,:,2)));
max_q = max (max(image_yiq(:,:,3)));

%Renormalize the image again after the multipication
% to [0,1].
image_yiq(:,:,1) = image_yiq(:,:,1)/max_y;
image_yiq(:,:,2) = image_yiq(:,:,2)/max_i;
image_yiq(:,:,3) = image_yiq(:,:,3)/max_q;

I can't understand why the matrix multiplication fails. I want the code to be nice and not just to, multiply the matrix by hand...

Answer 1

You try to multiple a 3D array with the matrix you created which is not a proper matrix multiplication. You should unfold your image data to a 3-by-m*n matrix and multiply it with your custom matrix.

Here is a solution for applying custom color space conversions to an RGB image. I used the matrix that you provided and compared it to the built-in YIQ transform.

%# Define the conversion matrix
matrix = [0.299  0.587  0.114;
          0.596 -0.274 -0.322;
          0.211 -0.523  0.312];

%# Read your image here
rgb = im2double(imread('peppers.png'));
subplot(1,3,1), imshow(rgb)
title('RGB')


%# Convert using unfolding and folding
[m n k] = size(rgb);

%# Unfold the 3D array to 3-by-m*n matrix
A = permute(rgb, [3 1 2]);
A = reshape(A, [k m*n]);

%# Apply the transform
yiq = matrix * A;

%# Ensure the bounds
yiq(yiq > 1) = 1;
yiq(yiq < 0) = 0;

%# Fold the matrix to a 3D array
yiq = reshape(yiq, [k m n]);
yiq = permute(yiq, [2 3 1]);

subplot(1,3,2), imshow(yiq)
title('YIQ (with custom matrix)')


%# Convert using the rgb2ntsc method
yiq2 = rgb2ntsc(rgb);
subplot(1,3,3), imshow(yiq2)
title('YIQ (built-in)')

Note that k will be 3 for RGB images. See the size of the matrices after each statement. And don't forget to convert your image to double.

Answer 2

It is possible to do this with Imagemagick using the same matrix and -color-matrix function:

Input:

convert peppers_tiny.png -color-matrix \
" \
0.299 0.587 0.114 \
0.596 -0.274 -0.322 \
0.211 -0.523 0.312 \
" \
peppers_tiny_yiq.png

But this is not a true sRGB to YIQ transformation.

Here is an sRGB to YIQ transformation, showing the YIQ as if RGB:

convert peppers_tiny.png -colorspace YIQ -separate \
-set colorspace sRGB -combine peppers_tiny_yiq2.png

Here is the same but swapping the first two channels:

convert peppers_tiny.png -colorspace YIQ -separate \
-swap 0,1 -set colorspace sRGB -combine peppers_tiny_yiq3.png