In Matlab, how can I use chroma subsampling to downscale a 4:4:4 image to 4:2:0 when the image is in YCbCr?

Question

I have already converted the jpg images from RGB to YCbCr but must now use Chroma Subsampling to make them 4:2:0. I have searched but have not found any information on how to do this (note: I am very new to Matlab)

Edit: I now have this but at the bottom where I am setting ycbcr(:,:,2) = newCb it says "Unable to perform assignment because the size of the left side is 1273-by-1910 and the size of the right side is 1273-by-955-by-0."

function f = conversion(source_image, source_name)

image = imread(source_image);

% conversion_matrix = [0.299 -0.168736 0.5;
%                      0.587 -.0331264 -.0418688;
%                      0.114  0.5 -.081312];

conversion_matrix = [0.299 0.587 0.114;
                     -0.168736 -.0331264 0.5;
                     0.5  -.0418688 -.081312];

ycbr = reshape(double(image),[],3)*conversion_matrix;

ycbr = reshape(uint8(ycbr),size(image));

Y = ycbr(:,:,1)+ 0;
Cb = ycbr(:,:,2)+ 0.5;
Cr = ycbr(:,:,3)+ 0.5;

Cb = double(Cb);
newCb = uint8(round((Cb(:,1:2:end, 1:2:end) + Cb(:,2:2:end, 1:2:end) + Cb(:,1:2:end, 2:2:end) + Cb(:,2:2:end, 2:2:end)) / 4));
Cr = double(Cr);
newCr = uint8(round((Cr(:,1:2:end, 1:2:end) + Cr(:,2:2:end, 1:2:end) + Cr(:,1:2:end, 2:2:end) + Cr(:,2:2:end, 2:2:end)) / 4));

ycbcr(:,:,1) = Y;
ycbcr(:,:,2) = newCb;
ycbcr(:,:,3) = newCr;

imshow(ycbcr);
imwrite(ycbcr, source_name);

f = ycbcr;

Answer 1

You can simply resize Cb and Cr by a factor of 0.5 in each axis:

Assume:

YUV = rgb2ycbcr(RGB);
Y = YUV(:, :, 1);
U = YUV(:, :, 2);
V = YUV(:, :, 3);

Y channel is unmodified (same Y for 4:2:0 as in 4:4:4 format)

Down-sample U and V by a factor of 0.5 for getting 4:2:0 format:

newU = imresize(U, 0.5);
newV = imresize(V, 0.5);

In MATLAB you usually like to keep the 420 result Y, newU, newV and 3 matrices (planar format), and not merge the matrices into one matrix.

The 4:2:0 format doesn't dictates specific components ordering (like I420, or NV12...) so the three matrices are considered to be in 4:2:0 format.

---

Down-sampling without using imresize:

You can Down-sample U and V using the following code sample:

U = double(U);
newU = uint8(round((U(1:2:end, 1:2:end) + U(2:2:end, 1:2:end) + U(1:2:end, 2:2:end) + U(2:2:end, 2:2:end)) / 4));

Result is equivalent to resizing with bi-linear interpolation, without Anti-aliasing filter:

shrunkU = imresize(U, 0.5, 'bilinear', 'Antialiasing', false);

---

Update:

• The conversion formula you have posted is incorrect (at least not the same as MATLAB builtin rgb2ycbcr conversion formula).
  MATLAB conversion formula matches BT.601 "limited range" standard.
• It also looks like you have a mistake in the vector by matrix multiplication.
• As I commented, I recommend you to save the 420 result to binary file.

The following code sample performs the following steps:

• Convert RGB to YCbCr without using builtin function, and compare the result to MATLAB rgb2ycbcr result.
• Convert from YCbCr 444 to YCbCr 420 (without using builtin function).
• Save the 420 result to binary file im.yuv
• Convert im.yuv to PNG format using FFmpeg command line tool, and show the result.

Here is the code:

RGB = imresize(imread('autumn.png'), [100, 170]); % Load RGB image for testing (and resize)

% Convert to YCbCr using MATLAB builtin function (used as reference)
refYUV = rgb2ycbcr(RGB);

% Conversion matrix applies BT.601 standard ("limited range").
T = [ 0.2568    0.5041    0.0979
     -0.1482   -0.2910    0.4392
      0.4392   -0.3678   -0.0714];

% Conversion offset (for "limted range" standard the offset for Y channel is 16)
offset = [16
          128
          128];

% Manual conversion from RGB to YCbCr (YUV is a shortcut name from YCbCr):
% Multiply T matrix (from the left side) by three "long rows" of RGB elements and add offsets vector.
YUV = T*(reshape(double(RGB), [], 3))' +  offset;

% Reshape YUV to the shape of RGB, and convert back to uint8.
YUV = uint8(reshape(YUV', size(RGB)));

% Verify that YUV equals refYUV (maximum difference result is 1 out of 255)
disp(['Max Diff = ', num2str(max(imabsdiff(YUV(:), refYUV(:))))]);

% Convert to YUV 420 (without builtin function):
Y = YUV(:, :, 1)
U = double(YUV(:, :, 2))
V = double(YUV(:, :, 3))
newU = uint8(round((U(1:2:end, 1:2:end) + U(2:2:end, 1:2:end) + U(1:2:end, 2:2:end) + U(2:2:end, 2:2:end)) / 4));
newV = uint8(round((V(1:2:end, 1:2:end) + V(2:2:end, 1:2:end) + V(1:2:end, 2:2:end) + V(2:2:end, 2:2:end)) / 4));

% Save result to YUV file (file format is going to be raw I420 foramt):
% Make sure to transpose the matrix before saving (becuase MATLAB is "column major", and fomrat is "row major").
f = fopen('im.yuv', 'w');
fwrite(f, Y', 'uint8');
fwrite(f, newU', 'uint8');
fwrite(f, newV', 'uint8');
fclose(f);

% Convert im.yuv to PNG format using FFmpeg (free command line tool).
% For Windows system, download stable stsatic build from https://ffmpeg.zeranoe.com/builds/
% Place ffmpeg.exe in the same path of the script (just for testing withing MATLAB)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[status, cmdout] = system('ffmpeg -y -s 170x100 -i im.yuv -pix_fmt yuv420p im.png');

% Read and show im.png for testing:  
I = imread('im.png');
imshow(I)

---

Result (after converting to YCbCr 420 and converting back to RGB using FFmpeg):