You can see how TMW does it with
open rgb2gray
The entire function is available for you to read.
Also, there are many color map manipulation tools available. See the documentation for
colormap
gray <- This one especially
That should point you in the right direction. (There is example code in the help for these functions)
If you need to literally do the math yourself, it boils down to matrix manipulation. You could brute force it by adding the R, G, and B matrices together and dividing by 3. That would give you some approximation of a brightness matrix, which is essentially the image in grayscale.
You can experiment with how you weight each color channel to get different results (kind of like using filters with black and white film).
Good luck!
