The easiest way to get a black and white image is to use Photoshop’s de-saturate command.  This strips all color information out of the image, leaving only a grayscale residual.  You will however find that the de-saturate operation is unsatisfactory. De-saturate converts color information to grayscale information by taking an average.   Each pixel in an RGB color image is represented by a 3×1 vector (or array,) generally on a 0-255 scale, with each entry of the vector corresponding to the intensity of red, green, and blue, respectively. So          [ 255 0 0 ] represents pure red; [0 255 0] represents pure green; [0 0 255] represents pure blue.  These vectors are orthogonal and so span the entire color space, meaning any imaginable color can be created as some linear combination thereof. The de-saturate command converts these three-dimensional vectors to a one-dimensional grayscale vector by averaging the color information, perhaps using the root mean square:

This quickly causes a problem — the grayscale values of pure red, pure green, and pure blue are all the same!  Moreover, there are practically infinitely other colors sharing the same grayscale levels — this red [ 200 25 30 ] and this green [ 30 200 25 ] among them (both would be [ 177.7 ] in this scheme).    Only pure white [ 255 255 255 ] and pure black [0 0 0 ] are uniquely defined as grayscale vectors [ 255 ] and [ 0 ], respectively.

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