Calculating & visualizing the Perceived Brightness of a Color Image (RGB) in MATLAB

Calculating the Perceived Brightness of a Color Image (RGB) in MATLAB  or in simple words,
calculating the brightness of an RGB color image.

Before implementing it in matlab, we must know the conversion formula,

RGB -> Luma conversion formula. (more weight-age to green since our eyes are more sensitive to green color.)

Photometric/digital ITU-R:
(Here 0.2126+0.7152+0.0722=1)
(Source: en.wikipedia.org/wiki/Relative_luminance)
Y1 = 0.2126*R + 0.7152*G + 0.0722*B

Digital CCIR601 (gives more weight to the R and B components):
(Here 0.299+0.587+0.114=1)
(Source: www.w3.org/TR/AERT)
Y2 = 0.299*R + 0.587*G + 0.114*B

If ready to trade accuracy with performance, there are two approximation formulas above two:
(Source : Franci Penov answer )
Y1a = 0.33*R + 0.5*G + 0.16*B
or Y1a = (R+R+B+G+G+G)/6

Y2a = 0.375*R + 0.5*G + 0.125*B
or Y2a = (R+R+R+B+G+G+G+G)/8

Our Test Image is an RGB image: 225x609 in size Our Test Image is an RGB image 225x609 in size

Suppose we have read the above image through imread( ) function & stored it in a variable named 'x' .
>> x=imread('image.jpg'); %assuming that this image lies in working directory & named "image"

now size(x) will give result as,
ans =   225   609     3

NOTE: The third element displaying a value of '3' denotes the presence of 3 planes of 225x609 matrix. 1st of which the red (R) plane (designated by value 1 in the 3rd index of x), 2nd is the green(G) plane (designated by value 2 in the 3rd index of x) & 3rd is the blue (B) plane (designated by value 3 in the 3rd index of x) .

In order to access three color planes separately, type your formula like this x(:,:,1) or x(:,:,2) or x(:,:,3). See more about this at: Using MATLAB, Extracting individual Red, Blue & Green (RGB) planes, From a RGB Image, With Code

Now how to apply above three formulas?

Applying Y1 = 0.2126*R + 0.7152*G + 0.0722*B in MATLAB our command will look like,

>> Y1=0.2126*x(:,:,1)+0.7152*x(:,:,2)+0.7152*x(:,:,3);
%to access a particular pixel luma/brightness value calculated by above formula use the command as,

>>Y1(200,200)
ans =  116

%thus perceived brightness at (200,200)pixel location is 166 in a scale of 255.

% Now since its also stored as an image we can visualize the Brightness values of the image as,

>>imshow(Y1)

The above 2 lines of code will result in another image having a single luma plane, which look like this. Perceived Brightness of a Color Image (RGB) in MATLAB  by Formula 1

Applying Y2 = 0.299*R + 0.587*G + 0.114*B in MATLAB our command will look like,

>> Y2=0.299*x(:,:,1)+0.587*x(:,:,2)+0.114*x(:,:,3);
>>imshow(Y2) % to see visualize the brightness Perceived Brightness of a Color Image (RGB) in MATLAB  by Formula 2

The above image came to be more darker than Y1 case, due to the fact more weight-age is distributed among R & B value than G.