Clever to start out with a greyscale image! But it still poses some constraints, let's say if we start with an all black image for an edge case to demonstrate the limitations, we can only have a 2D pattern in the 3D space, right?

However the luminance component of the image could probably be adjusted within certain error margins and vice versa. Perhaps by some form of bruteforce!

To know for sure I suppose coding is needed!