Questions about the rgb2gray function

I am trying to convert the RGB pixel (120, 119, 112) to gray pixel, When using the conversion equation '0.299 * R + 0.587 * G + 0.114 * B' provided by the function document, as following codes shows,

uint8(120 * 0.2989 +119 * 0.587 + 112 * 0.114)

the results is 118. But when using rgb2gray function as follows,

im2gray(aa)  % aa is a 1x1x3 matrix [120, 119, 112]

the results is 119.

Does anyone knows why? Thanks!

Answer 1

[Stephen23]

"does anyone know why?"

The values shown in the documentation are shown only to 3 decimal places.

The actual values used for the conversion are:

format long G
M = inv([1,0.956,0.621;1,-0.272,-0.647;1,-1.106,1.703]); % inv of YIQ->RGB
C = M(1,:).' % the actual values

C = 3×1

0.298936021293775 0.587043074451121 0.114020904255103

[120,119,112]*C

ans = 
          118.500789691508

im2gray(cat(3,120,119,112)/255)*255

ans = 
          118.500789691508

And if you are wondering where that matrix comes from, take a look at the conversions here:

https://en.wikipedia.org/wiki/YIQ#From_YIQ_to_RGB

[志远 任]

That's really helpful, thanks a lot!