What is the actual ratio of color channels used in function rgb2gray?

I was curious to know the actual ratio of color channels used in rgb2gray function. The documentation mentioned about the ratio used in the function i.e.

(0.298936021293775 * R + 0.587043074451121 * G + 0.114020904255103 * B)

(0.299 * R + 0.587 * G + 0.114 * B)

To confirm it I wrote a script. Two gray image histogram are compared where one gray image is generated using inbuilt rgb2gray function and other gray image is generated using the mentioned ratio of color channels.

path = "OG/550_img_.png"; 
img = imread(path);

gray1 = rgb2gray(img);
gray2 = 0.298936021293775 * img(:,:,1) ...
          + 0.587043074451121 * img(:,:,2) ...
          + 0.114020904255103 * img(:,:,3) ;

plot(imhist(gray1),color='r');
hold on;
plot(imhist(gray2),Color='b');

As you can can see from the figure the histogram is not matching. So what is the actual ratio used by rgb2gray function?

Answer 1

[Constantino Carlos Reyes-Aldasoro]

This is interesting, it looks like rgb2gray is rounding or filtering in some way.

[Abinas]

You are right. I tried the following.

path = "OG/550_img_.png"; 
img = imread(path);

gray1 = rgb2gray(img);
img = im2double(img); % new
gray2 = 0.298936021293775 * img(:,:,1) ...
    + 0.587043074451121 * img(:,:,2) ...
    + 0.114020904255103 * img(:,:,3) ;

gray2 = im2uint8(gray2); % new


plot(imhist(gray1),color='r');
hold on;
plot(imhist(gray2),Color='b');

And now the histogram matches exactly. Thank you.