Am I understanding this correctly?

If I start with a color picture and do the below. It separates the original color image into the three red, blue and green matrices with each matrix being a grayscale matrix. When I imshow the red one, if the pixel value is high on it (white) and low for the other two on the exact same pixel then that pixel in the original color image is red right?

r = color(:, :, 1); 
g = color(:, :, 2); 
b = color(:, :, 3);

Answer 1

[Matt J]

If by "low" you mean zero and by "high" you mean 255, then yes.

Answer 2

[John D'Errico]

Yes. Colors that you would describe as red all have high values in the red channel, and small values in the green and blue channels. But those values need not all be strictly [255 0 0]. (Or [1 0 0], depending on the scaling you use.)

For example, using a [0,1] normalization...

img(:,:,1) = 1 - .2*rand(100,100);
img(:,:,2) = .2*rand(100,100);
img(:,:,3) = .2*rand(100,100);
imshow(img)

You might reasonably call that entire image red, just various shades thereof. And the limits of what you might call red are probably subtly different for you than for me. The boundary of the set you would describe as red is indeed in that corner of the RGB color space though.