When you interpret a 2D data array as a grayscale image, then you assume that the contributions of R, G, and B are all equal.
RGB = repmat(grayscale, 1, 1, 3);
equal red, green, blue contributions in RGB images show up as gray to humans.
When you take a colorplane out of an RGB image and put it into a different RGB array with the other two planes set to 0, like in method 2, then the value of the other two planes is 0, not "the same" as the plane that you kept. That will show up as monochrome planes of the major color, not as grayscale.
Sum = R+G+B;
When you have zeroed the other two color planes then when you add the 3D arrays, you just reproduce the original RGB image. There is the G and B have 0 in their red planes, so the red plane of Sum would effectively just be copied from the red plane of the original image.
greySum = X(:,:,1)+X(:,:,2)+ X(:,:,3)
the value associated with the red contribution gets added to the value associated with the green and blue contributions. The contributions interfere with each other.
Your imread() of the .jpg is going to return a uint8 array. When you add the three uint8 arrays together, the locations are going to "saturate" -- any sum that would have exceeded 255 is going to be set to 255. This results in a lot of bright areas on the resulting image.
If you were to use im2double() as you read in the image, then you would not get saturation of the double() data class. You would, however, get results in the range 0.0 to 3.0, and when you go to display, any result above 1.0 would be treated as 1.0, so you would get the same kind of bright saturation. However, you could do
greySum = (X(:,:,1)+X(:,:,2)+ X(:,:,3))/3;
in that case to get something in the range 0 to 1. This will not work for uint8 data.
Note that using
greySum = (X(:,:,1)+X(:,:,2)+ X(:,:,3))/3
will not be the same as rgb2gray() . It turns out that Green is responsible for more of our sensation of brightness, followed by red, and that blue does not give much contribution to brightness. When you add them weighted equally, you over-represent blue and red contribution to brightness.
